Best first opening repertoire for beginners to improve

It sounds like you already know what you want. Why not just search for openings that are most in fashion among GMs and teach those? They wont be bad and you'll have a lot of recent material. As a wise man once said, "Teaching is like sex- ethusiasm is more important than technique!" If you believe in the choices your students will pick up on it and study harder too.

Because chances to understand them, and play them properly are exactly zero percent- that simple.

 It doesn't seem best to me as well. But the original poster seems to want that answer. My impression is that he was asking the question as a way to clarify his own ideas. If he gets good results that way I'm happy to be proven wrong.

It depends on what kind of game you like.  There's no "best" opening, there are just a host of sound ones, and each offers different advantages and drawbacks.

With white, you can play 1. e4, 1. d4, 1. Nf3 (the Reti), 1. c4 (the English), or if you're the type who gets better results with black, you can even play 1. a3 (Anderssen's).  The Experts in my area often give their better students the Reti or the English to start off with, so that they can "book up" (i.e. study opening lines) for the 1. e4 e5 openings or the Sicilian defense, or the various Queen's gambit declined lines.  Hypermodern openings are flexible, and less well-studied, but just as sound as the predominant classical openings.  No one learns much from falling into one opening trap after another, aside from learning how to punish unsound play, which has little use beyond the C-rank.

The other good thing about it is that the Reti and the English prepare you to play the more popular defenses against 1. e4  and 1.d4, those being the Sicilian Defense and the Indian Defenses, respectively.

Have a look at his other threads, this is the usual fare afaik

Needless to say, I disagree with you. You need your beginners to get to open positions where they know roughly what to do without having to teach them loads of stuff. 3. Nc3 against the French and advance Caro Kann will lead to closed positions they don't understand. Lopez is fine, of course. Add for black, 2. ... Nc6 means they have to know a lot to not get squished, like how to deal with 3. Bc4 Nf6 4. Ng5 which is not easy for a beginner and could be quite off-putting for them. You get more open positions from the Tarrasch than the semi-slav so it's more suitable for helping develop their tactics. 

You shouldn't be prioritising popularity over open-ness and you do need to give them some lines where they are likely to know a bit more about the position than their opponents so they get the moral boost that inevitably leads to. The openings I suggested are all sound, mainstream, open, and full of themes that will be relevant to them forever. There is nothing there that would shock the commentators if Magnus or Anand played it. 

I have never suggested just blindly choosing the openings that are most in fashion among GMs whatever they may be. But the French Exchange Monte Carlo (4.c4) is literraly a QGA a tempo down, White is literally already worse... You might as well recommend 1.e3 e5 2.e4 transposing to the Open Game...

The French Exchange Monte Carlo (4.c4) is definitely not mainstream at all. In my database of players rated 2600+ between the year 2016 and 2020, there are 12129 games, 421 French, 35 Exchange variation, 0 Monte Carlo (4.c4), compared to 251 3.Nc3 and 100 3.Nd2. So it would be surprising if Magnus or Anand played it.

If we tell beginners to play such crap openings it would go against that famous proverb that we often repeat them: "always play the best move". Can there really be no middle ground? Aren't there some openings that are BOTH good for beginners and currently popular among GMs?

That the Tarrasch be the only defense that is good for beginners against 1.d4 is impossible to believe since there are so many defenses against 1.d4.

white is not worse in the Monte Carlo French. It’s playable for white, he’s not down a tempo compared to anything roughly equal imbalanced position 

Now that I think about it maybe the point of this thread was for us to suggest a beginning repertoire for you...  

You can’t go about asking us for all these answers and then aggressively shoot down the ones we give you; otherwise if you’re so wrongly headstrong why ask the question at all? You can be the one asking the questions or the one answering. 

Morozevich played 4. c4 in the exchange French in 2016. In fact, Grandmaster Alexandr Rakhmanov (FIDE 2645 [which you'll note is 2600+]) has played this line with white repeatedly - at least 12 times in the last 4 yours. Your database is flawed. Where did you get it? 

Also, Yusupov played the position against Kasimzdhanov in 2005 - Yusupov knows his openings, and wouldn't play a system that left him worse - he's famous for picking lines that can give him a long-term edge in sound positions. It's actually interesting to see how the Yusupov position arose - it was from an Albin Counter Gambit. What this tells you is that this position can arise from a number of different openings, and (Grandmaster) white players wouldn't be aiming for it from those different openings if it was no good. 

Incidentally, white wouldn't be a tempo down in the QGA: 1. d4 d5 2. c4 dxc4 3. e3 e5 4. Bxc4 exd4 5. exd4 is the same position with the same move count / same side to move as 1. e4 e6 2. d4 d5 3. exd5 exd5 4. c4 dxc4 5. Bxc4. 

No-one said the Tarrasch was the only thing to recommend against d4, but it's a good recommendation as I explaned - it give black good chances of getting a fairly open position which is what beginners need. 

Your knowledge of openings is clearly not yet that extensive (keep at it, you'll get there, everyone starts from the beginning in the beginning), and your database of games is clearly not that good (if you can afford it it might be worth investing in a better database). It's good that you're asking for help with your opening repertoire, I hope I've been of some help. 

The move you gave, 4...dxc4, is idiotic. Obviously if Black is not completely stupid he will wait until White moves his f1 Bishop (to d3 or e2) before playing ...dxc4 and thus White will have lost a tempo. And so since you believed that the flawed line you just gave is playable for White then surely now you must admit that the same line a tempo down is rubbish for White.

My database ("players rated 2600+ between the year 2016 and 2020") is not flawed, it is a filtered version of Chessbase's Mega Database 2020. The very few games you speak of didn't appear in my database because they are all blitz and rapid games, and my database intelligently excludes blitz and rapid games. By including blitz and rapid games, the only Monte Carlo games are 7 games by Rakhmanov (you said 12 but in 5 of them Black was less than 2600 Elo) and 1 game by Morozevich (all of them blitz and rapid), and that's it, this is not just a few examples, this is the exhaustive list. The fact that all the Monte Carlo games happen to be blitz and rapid speak volume as to the quality of this opening.

Also notice that absolutely none of them began with 1.e4, which is an additional argument against the Monte Carlo: if you advocate that beginners always play 1.e4, it is a bit strange to then tell them to transpose to an opening that is more often reached through 1.c4 and 1.d4, as most 1.e4 players prefer to stay in pure 1.e4 territory.

The fact that it has been played a tiny amount of times by 2600 Elo players doesn't prove that it is good, otherwise 1.a4 would be good since it has been played by World Champion Magnus Carlsen, yet I am sure you must agree that 1.a4 does not correspond to your principle of "openings that they can keep playing forever [...] that will serve them for a lifetime if they want it to".

Anyway you are grasping at straws, the fact that the Monte Carlo has been played a tiny amount of times is an argument against the Monte Carlo not for it. You need to compare its popularity to the popularity of White's other options, and as I already said ealier 3.Nc3 is 120 times more popular than the Monte Carlo, 3.Nd2 is 50 times more popular than the Monte Carlo, these ratios are just ridiculously huge and you just can't argue with them.

Engine evaluation is not very helpful so early, but for what it's worth I will mention that Stockfish 11 says the Monte Carlo is -0.16 which agrees with my view.

Anyway, I have considered your suggestion of the Monte Carlo, and I have rejected it, all in good faith. It's no use insisting on it. I ask for other suggestions.

Ok, I am a little hesitant to chime in since I am much lower-rated than many here, but I have found that QG for white and Scandinavian for black has been fairly easy to get to playable middlegames at my level.

I doubt there's a "best" for all...anything.

Keeping it simple and yet having something to study long term should good.

Won't be popular, but...

White 1.d4

Black 1...c6 vs everything 

If sharp tactical openings are what's best for beginners, would the Sicilian Najdorf be good for beginners? Curiously I never see this opening suggested.

The Najdorf is much more than a "sharp tactical opening"- actually there are lines that white may enforce which are not tactical at all.

Problem with Najdorf as a beginner, you'll never get to play it.

problem with trying to play any sicilian is, you never get to play the line you want to play.