The position.
Do you play against the opponent or the position?

The position. I always assume my opponent will make the best move possible except when I've made a serious blunder and my only chance to save the game is an all out attack where he may make a mistake.

Sometimes the persons's rating skews your evaluations. Sometimes knowing someone's preferences you'll opt for a different opening or type of middlegame, but other than minor things like this it's pretty much only the position.
Not only the position in the sense of solving problems the opponent poses, but also in a collaborative sense, the position tells you what it wants or needs to happen.
"... In the majority of positions, there are a number of possible moves of roughly equal merit, ..." - GM John Nunn (2014)

I disagree, chess is also a psychological game. Recently, I saw a possible checkmate I could deliver, and I had to give my queen away, but more precisely, my opponent had to take my queen with his pawn, instead of his queen, which was facing my queen. At first it sounds obvious to not exchange queens but rather take your opponents queen with your pawn if that's possible. But I wasn't sure if my opponent had seen this tactic, and the checkmate was only possible if he took my queen with the pawn. So I had to make it look like a mistake, and hoped he wouldn't take my queen with his queen. I did my move, placed my queen in front of those pawns, and then I wrote in the chat: "Damn, forgot those pawns. "
I don't think that's cheating however.
So yes, I wouldn't say you always play against a position, but also against the opponent. I also play differently when I play against friends, because I know how they play. It doesn't mean I don't play against the position too, you can play against both at the same time. But being conscious of who they are, how they play, how they react and eventually even influence this (like in the chat I mentioned before), is just another factor you must consider, see it like a chess move you're doing, you're just thinking ahead and it's one more point you're being aware of and taking for your advantage, without excluding the fact that you're playing against the position at the same time and always expecting them to make the best move. That's how I see it at least!

Both. Objective good moves in the middlegame/endgame, and confront your opponent with an opening he dislikes. I think my approach/aim is to play to my opponent's weaknesses since I consider myself to be a fairly all-round chessplayer.

If you are familiar with an opponent, you try to steer into positions you know they don't like. One of my friends loved to use his knights, and I often would try to trade his knights off to blunt that tactic, him bothering me with knight forks. As I got stronger, i would sometimes let him waste time and material playing with his knights while I tryed to find attacking moves against his king.

Informal survey: When you play chess, do you consider yourself to be primarily competing with your opponent or solving a series of positional problems?
Position, always. But it does help if you know your opponent's tendencies.

Informal survey: When you play chess, do you consider yourself to be primarily competing with your opponent or solving a series of positional problems?
Informal survey: When you play chess, do you consider yourself to be primarily competing with your opponent or solving a series of positional problems?