AsalamuAlaykum Warahmatullahi Wabarakatuh,
If we were at the bottom of the stairs, i'd rather have the brother go up first than stand there and watch me go up first, but I still think it's polite if they wait, better than pushing past you or walking alongside you, I hate touchy people :thumbs_up
As for Non-Muslim brothers, they usually walk right next to you, when I'm with my momma they cross the road Lol, maybe it's cause of her niqaab, we say it from far away that such and such will cross the road jus before he/she approaches us, and they always do!! :statisfie It never happens when I'm just there, it's annoying because they're almost touching you when they walk beside you :-[
JazakiAllahu khair sis Ramz =) Hope you're feeling the Ramadhan spririt now Heh, *wub*