Curious h3!? reasoning?

h3 here is good, very similar to the quiet move h3 in some Queen's Gambit Exchange variation Carlsbad games (with 4 cxd5 exd5 played). In your position, White takes control of g4, so a Black piece can't land there, and secures a possible retreat for the Bf4, as well as making the undermining thrust possible, g2-g4 after some preparation. The exact same idea (taking control of g4, but in this system, to deny the Bishop on c8 any decent squares) is sometimes played in the aforementioned QGD exchange variation after White has placed a knight on e5 and then secured it with f2-f4 and sometimes following up with g2-g4 later after preparation. (this may have been known as the "Pillsbury" attack or something. Won some nice kingside attack lines with this kind of system.

This is probably because it is against chess.com's tos to discuss "religious or political debate" 

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Certain topics just tend to become controversial and attract trolls, so it is better to keep those topics in the appropriate clubs. Here are some you may want to check out: 

https://www.chess.com/club/the-ideas-room

https://www.chess.com/club/open-ideas

https://www.chess.com/club/lgbt-club

https://www.chess.com/club/lgbtqa-forever

There may be other clubs too. This was just my chess.com club search, so this is just what I found first. 

chess.com Staff/Mods don't mute/ban because they disagree with an opinion; they simply enforce chess.com's tos when those rules are not followed.

Your post resonated with me because I play the QG Carlsbad structures often and I like your explanation regarding the e5 Knight and following plan. I've had this come up in a few of my games, but in practice, I usually get h3 and little else moving on the kingside (f4 and g4 etc.) as I'm usually playing for the center f3-e4 pawn break, or playing thematic ideas on the queenside (based on the exact position).

Thanks for sharing your knowledge. I liked your QG exchange example.

I've seen similar ideas (as mentioned), but the h3 move wasn't intuitive to me here because of it weakening my castled King and similarly why I didn't calculate for ...Nd7 with ...g5. It wasn't even on my radar because I judged ...g5 as too weakening of their King and giving me extra targets and ideas to play against.

I'm familiar with many Dutch Defense and King's Indian Defense game examples of black advancing their kingside pawns in front of their castled King, but perhaps I just didn't expect that out of this particular opening (and position) here.

Aggressive counter-moves are thematic more for positions than for openings, though. However, in some of the King's Indian or Benoni defences, ....g5 is good for black because it inhibits white's K-side play. I'm playing 5 min chess only at the moment and am starting to use g4 as white more and more. That sort of thing is very effective against people who try to win on time.

yes but the people who were arguing for the other side never received a punsihment? is this due to carelessness or bias?

It could be to stop h5, Nf6 and Ng4? Looks dumb but it's a pretty closed position and the slow kingside expansion looks like a threat.

the dark-squared bishop is an important defender on the kingside, i guess h3 preserves the bishop to prevent nxg3 and black get a huge attack

You wouldn't make the weakening move h3 if the B is a defender. White wants to keep the pieces on (and provide support for an eventual g2-g4, which could come after 5, 10 or even 15 moves) to increase his chances of a win.

Ya basically

Key takeaways

1. Bishop pair(luft for bishop) from immediate danger on sight

2.Making black s pawn avelanch difficult (can also be argued h3 is a hook for black s pawn storm but not here) 

3.preparing h3-g4 pawn push for white in future to open the LSB 

Obviously h3 is by far the best move here because of concrete reasons of preventing g5 and taking the bishop .. So ya.. Calculation is important...