We have a couple of vegetarians in the family and at family barbecues, 2 barbecues are used and as our get togethers start at about 12 and finish later in the evening, having several courses, my sister always makes a vegetarian chilli and the veggie members often bring their own veggie burgers etc as their contribution.
To me, if you invite guest to your home and for whatever reason they choose not to eat meat, you cook either a dish that everyone can eat that is vegetarian, with meaty accompaniments or just do a separate veggie dish - even if it's a shop bought one!
My son is gluten and dairy free, my nephew is dairy free. If they came to your house, would you expect them to eat the same food as you do, with the prospect of making them unwell?