Courtesy is simply that. It ought to be returned with thanks

Doesn't matter which sex the courtesy is extended to either.
I don't expect a gentleman to give me his seat, though if offered, age dependant, I'll take it with thanks, but after years of established behaviour I do expect to be passed to the inside when walking with a man, even my sons do it, and they seemed to know to do it as soon as they were as tall as I am

I also expect that if I'm walking close in woodland the person ahead of me doesn't crash through and let the branches slap me, and no I don't want to hear the, "Then don't walk too close!", of the terminally can't be bothered to think of others. Conversation requires proximity unless one wants to lug a megaphone

I'll be careful for others too.
Help me with my bags ? if we share the load, then thank you

Open the car door for me ? If I'm in a posh frock and high heels and it's not easy getting out with dignity

or I've been sitting too long and the joints are aching and seized, then I'll thank you kindly
There are as many boors out there as there are whatever filcon called the rude females though.
Brash, thoughtless and discourteous aren't a sex specific set of character flaws.
As for the aggressively militant female getting on her high horse and railing at some hapless male, that's just arrogant posturing and rather silly. Wanting to be seen to be heard

Just like the boor who loudly proclaims, "Surely you can do it for yourself!" and lets the door slam closed
Neither realises that they're influencing no one in any positive fashion. Just too fraught to be worth bothering with.
To courteous strangers who create little happy feelings
cheers,
Toddy