Seems really normal to me. I, and family with kids have done this a lot.
But how does it start? Did you just go into the bathroom and start bathing your children? Or did you ask permission first? As someone who does not have children, this is bizarre.
And OP if you're not ok with it, then just because other people do it doesn't mean you have to do it. Like, if I feel something is weird, then I'm not going to do it because other people are doing it. I'm not a lemming...
My SIL actually started it in our family. Everyone in DH's family all live 1.5-2 hours from each other, and she asked to bath her daughter a couple of times before a trip home.
When we had kids, it sounded like a good idea to me - kids get a bath, if they go to sleep on the way home, we can throw them into bed, already in their pyjamas.
No-one makes a huge mess, using one towel and a washcloth isn't that much of an imposition.
I don't know what would be weird about it.