At our home I always clean the grill after every use anyway so I just cook my stuff over to the side.
Over the extended families homes, they generally try to keep my food separate which I appreciate.
I've never been invited over friends homes for BBQ's. My guess is they think I would naturally just not want to be over there. lol Dinners, yes, BBQ's, no.
Being that my husband and mother eat meat, our pans and dishes have all had some contact with meat. They're cleaned after every meal though so it doesn't really bother me. If they want to make meat for their part of dinner, I generally cook mine first and they use the pan second.
I wouldn't want my food to come in direct contact with meat juices, but, on high temperatures like a grill, the juices are pretty much non existant on the actual grill. I'll be honest and say I have *never tasted any meat tastes on my veggie burgers when they were cooked on the grill with other meat nor has it ever made me queasy after eating it. That's enough to convince me that no actual juices are lingering on my food.