I think my issue with this idea is I can't imagine hosting a party where I didn't know my guests well.
It's actually not too hard depending on the type of party, and the back-yard BBQ, I think, is one of the most common cases for this.
I've often held parties with fairly open invitations - I'll invite all the grad students, for example, or everyone from choir. Throw in their families, which I may or may not have met, and there's a fair number of people whose dietary habits I'm not familiar with. There's also the case of being the organizer for a broader party - for work, or school, or any sort of larger group.
What I would do as a BBQ host/organizer is have enough veggie substitutes for about 20% of the group, and put out a tray of the veggie substitutes labelled 'vegetarian'. I would also label various other dishes according to what they contain - "contains cheese", "contains soy" and so on, making sure that there is a variety (ie, not all the sides contain wheat, and some are vegan). I might keep a few veggie burgers aside for if they run out quickly.
After that, I won't worry about it too much. I've made a good effort to see that people with different dietary requirements have food to eat, and that the food is clearly labelled. Whatever happens after that is no longer in my control. I wouldn't overbuy the veggie substitutes by too much, because that will almost always lead to wasted food, plus, as others have said, the veggie versions are usually significantly more expensive that meat versions. If the veggie burgers do run out, there are enough vegetarian sides so that people won't go hungry.
Oh, and the vegetarian side dishes would be intended for everyone, not just the vegetarians - things like corn on the cob, or chips and dip, or vinegar based coleslaw.