I'm not very superstitious myself. I would treat other people's superstitions as preferences, and accommodate them accordingly; my goal would be to minimize inconvenience to myself, but at the same time I wouldn't want to completely disregard what they want. Sorry to be wishy-washy about it!
It seems situational to me. For example, I have a friend who always says a quick prayer over her food (NOT calling that a superstition, just that it falls in the larger "preferences" category), and while I don't join her in doing the same, or refrain from eating my own meal, I sit there quietly and don't speak until she's done. If I was walking with someone and their preference was to cross the street to avoid a black cat, then cross back
to continue our journey, I would let them do what they felt they had to do without mocking them, but I personally would just keep walking straight.
For the stairs thing (never heard of that, btw), I don't think I would change my behavior much. If there was physically plenty of room for us both on the stairs I would just proceed up (or, more likely, down) and if that bothered them, they could go back to their landing and wait. Presumably I'm taking the stairs in order to get someplace, so why should I delay that; also, I feel a little wobbly on stairs anyway, so I'm not going to do any backtracking that might make me wobblier, if there's plenty of room. But, I wouldn't roll my eyes at the person or anything.
Once I had a co-worker who was really into the "knock on wood" thing. I'd heard of it, but I didn't really understand it. Like, you say something like, "I hope there's good weather for our picnic tomorrow," and that's kind of like "tempting Fate" to make it rain because you're counting on it not
raining, so you rap your knuckles on a wooden desk or something... for luck? Anyway, my co-worker was always saying it and knocking on wood. Okay, whatever, that's her thing. Then one day we were sitting somewhere at a non-wooden table, and conversation was such that she felt knocking on wood was required. She says to me, "Can you reach behind you and knock on that wooden cabinet for me?" And I was just like, "No." She stopped saying it as often after that. I would listen to her do it all the time, but I drew the line at going out of my way (however small) to do this thing for
her, which I personally didn't see the point of.