This isn't just based on an idle observation. I've tested it using a custom pwhexe&scenario to check that this was actually the case.
A 20 ship surface combat task force (4 BBs, 2 CAs, 4 CLs, 10 DDs) running through both narrow and wide straits. Not once were they fired on when there weren't any mines in the hex that contained the strait. The combat window opens and in the left corner where you get the "NAVAL MOVEMENT PHASE" etc. messages you get a "Naval Gun Fire at X" (X = base name) but, as I already said, nothing actually happens. Add mines to the straits and, boom, instantly the CD guns will actually start firing at the ships passing through.
There is no combat window, but the minesweepers will usually be hit by coastal gunfire, though it will not open a combat window, and the full extent of the exchange may not appear in the combat report of the player who owns the coastal guns.
The tests I've run were done in head to head mode so I can say with certainty that they didn't receive any damage at all.
Which straight hex are you referring to? I know for certain that I have run several different types of ships through Bataan into Manila with the allied coastal guns still there: both with mines at Bataan and without, and the presence of mines had no effect on whether the coastal guns fired or not. At night, in low moonlight, they often did not fire. With high moonlight, they usually fired.