Guess I'll start!
When I was newer to the game, I absolutely feared the bishop pin. I almost always played the prophylactic h3/...h6 or a3/...a6, to prevent any pin before it arrived.
I didn't like the tactical options that a pin gave my opponent, even if was only temporary. So I would spent time trying to prevent any pins before they could arise.
As I became more experienced, I started to see the pin as a "reason" to develop. So, if my opponent pinned my knight, I would think, "Thanks! Now I know where to put my own bishop."
So, at that point (intermediate level), I felt that allowing a pin helped me figure out how to develop my own pieces. I welcomed it.
Moving further in my development as a player, when I reached an advanced level, I began to see the pin as a dubious move from my opponent - because I started to slightly value bishops more than knights.
So I would allow the pin, then immediately put the question to the bishop with a pawn. "Are you willing to give up your bishop for my knight?"
At that point, I felt that, if my opponent exchanged pieces, then he would be "sacrificing the exchange" - giving up their more-valuable bishop for my less-valuable knight. And if they retreated the bishop, instead, then I felt that I had won a "free move" with my pawn move, gaining more space with minimal cost (which is often a useful pawn move in the future, regardless, to prevent endgame back-rank checkmates).
Now that I'm at an expert level, though, I've begun to experiment more with "leaving the bishop pin until the position clarifies further". I'm liking this approach, at the moment, because it leaves more options. I can put the question to the bishop with a pawn, if needed. Or I can break the pin with a bishop, or reinforce the knight with another knight ... or even move the pinned piece away and allow an exchange with doubled pawns - which would then offer a semi-open file for a rook to occupy ...
The only danger of this is that, by allowing the pin to stay for longer, there's a greater chance that the opponent can use the pin to further improve their position ... so my verdict is still up in the air ...
Ah, the bishop pin - familiar to chess players everywhere.
Players of all levels explore (or struggle with) this common tactic.
Some dislike it to the point of playing their pawns to h3/h6 or a3/a6 early on, just to stop the pin before it arrives.
Others welcome the pin and then like to "put the question" to the bishop afterward.
Others, still, ignore the pin and continue developing as if it isn't even there - feeling secure in the knowledge that they can "figure out how to deal with it later".
What about you? How do you like to handle the famous bishop pin?