I don't really buy the 'old person may be offended' line - while it is possible, I have certainly never seen anyone take obvious offence and I've been doing it for quite a lot of years! (Acceptance or polite refusal is what actually happens).
If they are offended, then that is their problem and they will soon get over it - it should be happening more often in the future.
I was also taught that it was good manners to give up your seat for an elderly person, and I think it is. If your manners are different, than that's your choice, but 'they might be offended' sounds like a poor excuse. (Apart from fat / possibly pregnant women - that can be a minefield!).
But, with small children, I understand that it is often better (for everyone!) for them to be sat at a table with something to do, rather than standing up and getting in everyone's way or wailing that they don't like standing.
Separate "Waiting Rooms" for "Ladies"?
They still have those. (Although, obviously, women don't have to use them). I don't think that is really relavant, though!