Liq

yeah, no.
If you're missing your foremast, say goodbye to sailing close hauled / turning upwind / let alone tacking
If you're missing your main mast, you'll be as quick as a turtle, waiting to get raked or hugged to death
Mizzen mast is not as crucial but then again it rarely gets focussed.
As others said, try to sail at an off-angle, so that you kind of still don't expose your sides but also don't give a clear shot to your masts. Worst thing you can do is either crossing at 90° so that your opponent can mastrake you, strike multiple mast hits in one broadside and possibly even get a mast or two. You also should not sail parallel to him, that way masts could be sniped efficiently.
Also, as said by others, as there is no mast-HP indicator, you kind of have to "count" the mast hits and estimate yourself how many more masthits you can take. That task becomes easier over time with experience, for example in the shallow waters, I know if my Surprise has taken 3-4 hits of 32pd carronades close up, it's time to repair.
Often, when people are going for your masts, especially mast-sniping, and they see the enemy using a rig-rep after scoring a couple mast hits, they get impatient and use the left-over shots on the hull - That's your chance to counterattack