Is is safe to wash your engine bay?

Perfectly safe - the engine bay is not sealed, so it gets sprayed with water every time you go through a deep puddle.

Obviously don't immerse the electrical bits in water, but wiping them over will be fine.

Caveat though - there is no point! Most of the filth in an engine bay is grease or oil, which water won't shift. You'd be better off with a proper degreaser.

Depends: If one uses a power washer and isn't cautious he can create quite a damage. While all electrical contacts are quite well isolated (the seals won't get better over time, so a 21 year old car hasn't certainly pristine seals) the high pressure jet of a power washer can enter the isolated zones (or bearings) and cause problems.

Washing with a proper degreaser, without power washer, should be fine