Honestly, everyone just being a little gracious is all you really need.
I’m vegan and I have no issues going to a normal bbq place for someone else’s party(though I don’t know what this place would be like). I can eat corn and undressed salad for a meal, I’ll survive. If the party were for me, I’d probably feel like it was passive aggression or a weird test though.
Similarly, there will be non-vegan food when I introduce my husband to my family and celebrate our wedding in my home country with a potluck, because one of my sisters has celiac’s and the other IBS, which restricts her fiber intake. I would have been totally cool with exclusively mashed potatoes (skin off) for dinner and sorbet for dessert, but I don’t think many others would be, and there’s not much else that works for all of us.
Sure, I could tell them not to bring non-vegan food, but that’s not very gracious, and I want people to be comfortable. They’d probably agree and either eat ahead of time or leave earlier and eat on the way home, so it’s not like there’s a practical difference in meat consumption, and it’s a great way to make people feel less welcome.