The chair pulling out is a bit naff IMO, dont really see how it helps anyone
Opening doors - I see that as non gender specific - I hold open a door for anyone coming in after me as do most people regardless of gender. and get up t o open a door if anyone else is going to find it difficult due to carrying a baby, pushing a pram, being disabled or frail elderly etc.
Ladies first seems more a tradition or courtesy used when some people have t o go first and everyone can't go at once - for example a group at a buffet.
If somebody said "for a change we'll have men go first this time - I wouldn't see that as a problem either.