Preventing opponent from castling in early game?

Is there any easy way to quantise how valuable it is to prevent your opponent castling - e.g. a bishop exchange where they have to take with their king/rook?

For instance if you get the opportunity to do this but it reduces your position, is it worth it in order to weaken the king and 'trap' the rook in the corner?

Of course not there is no easy way to quantify such things. Sometimes Black is able to play safely some consolidating moves, sometimes White's pressure is enough to provide long-term compensation for the material and Black struggles to untangle, there is no rule, it all relies on a concrete assessment of the position (and a bit of calculation).

The only rule I can think of is that the sacrifice of a pawn in return for castling is quite often sound, even if the compensation can look rather vague.

I agree with Nerwal, but to help illustrate his point, there are many opening lines where one players sacrifices material (often as much as a piece) to try to expose the other player's King. However, I believe most of those early piece sacrifices to prevent castling seem to be theoretically unsound, for example, the Fried Liver Attack of the Italian, where White sacs a Knight for a pawn. In the poisoned pawn variation of the French Winawer, however, Black sacs a pawn to try to weaken White's King's position and I believe that is considered more sound.

To clarify, I'm, mainly talking about straight exchanges rather than a sacrifice (other than maybe a pawn). e.g.

Maybe a poor example but here, white ends up with better position (more pieces developed) at the expense of losing the ability to castle. So if White allows this opportunity, is Kxf1 a good or terrible move?

If you can do it through a normal exchange you should.

But if you're looking for generic evaluations that apply to all positions (these don't exist), you should probably avoid giving up any material for it.

It's not meaningless. It still means white will struggle more to get his rook into play.

Pawn structures aren't static from move 1 to the end of the game. And tempos are tempos. It's another piece you're playing without, and an extra option unavailable.

Right, but there has been absolutely no resolution of the pawn structure so it's a huge stretch to call it a closed position. Black can try to open the position, and white may have to make concessions to keep it closed.

There are several mainstream lines where the white king stands on f1 after a few moves :

*the Benkö accepted : 1. d4 Nf6 2. c4 c5 3. d5 b5 4. cxb5 a6 5. bxa6 g6 6. Nc3 Bxa6 7. e4 Bxf1 8. Kxf1.

*the Nimzo-Dresden variation : 1. c4 c5 2. Nf3 Nf6 3. Nc3 d5 4. cxd5 Nxd5 5. e4 Nb4 6. Bc4 Nd3+ 7. Ke2 Nf4+ 8. Kf1.

*the English defence : 1. d4 e6 2. c4 b6 3. e4 Bb7 4. Bd3 f5 5. exf5 Bb4+ 6. Kf1.

*The Nimzo-indian : 1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. e3 b6 5. Ne2 Ba6 6. a3 Be7 7. Nf4 d5 8. cxd5 Bxf1 9. Kxf1.

White stands fine in all those lines. Except the Benkö line (which has been analyzed to great depth) I would even say it's easier to play as White there.