No I don't mind doing short shore dives with new divers. Though it is a struggle to get more than 10m on a shore dive locally so most people can last a fair while (there are deeper shore diving sites, but not for novices) but even if they didn't, I would be totally cool with it.
I'm not super excited about diving with new divers (new to diving or new to me) to be honest though, not one of those nice people
, as I have a few people I dive with regularly that I really enjoy diving with instead, but figure I won't meet anyone new just sticking to them.
I absolutely hate being paired with a new diver and/or an air hog on a boat though, given the cost, so I tend to only dive with people I know on boats. Sometimes I relent out of politeness and it hasn't gone well in a while... The last time the guy (who said he was experienced but I should have know after watching his descent that it was just talk) burned up a steel 12L tank in 10mins at 18m. On a shore dive no stress, but not on a boat dive I've paid $60 for, plus paid for nitrox fills and various other extra things I have to do for boat dives.
I try to be non pushy with more experienced divers than me too, when I have asked if I can come along for a dive, told them I understand if they prefer to dive with regular buddies and I won't be offended if they would prefer not to dive with me. I wish others would do the same as lately I've had a few people invite themselves along to more advanced dives I want to do, I've hinted really strongly that I would prefer not to dive with them, and if they don't get it I feel like such a horrible person when I have to knock them back more forcefully!