I doubt there are any planning restrictions though I do believe you need a big chunk of common sense here.
What you have to remember is a lot of barbies are portable so you would generally cook out of any breeze and maybe somewhere where there is shelter. This could be up against the boundary fence or whatever.
I would choose my location carefully in view of the fact that it will be permanent.
I accept that noseall's comment was light-hearted but, irrespective of their religious persuasion, I'd invite them anyway.
It's their choice to accept/decline the invitation and/or to eat/drink or not.
You wouldn't not invite a TT vegetarian (double negative) because of their dietary preferences, would you?