There are some amazingly self-centred and inconsiderate people in the world, aren't there? Yes, you, OP!
If your neighbour was lighting fires and burning rubbish in their garden you'd not be very happy about it would you? What you are doing is exactly the same - you are causing polution and bad smells to enter someone else's home. The likelihood is that all of your neighbours are unhapy with your cooking practices, but fear saying anything.
To those that think the neighbour is outrageous for even mentioning it, get yourself a life. How can you say someone just needs to shut their windows, in the middle of Summer, how will they cool down!? Your neighbour sitting in the garden puffing canabis would be the same problem - would you just stand that too?
It isn’t a problem the neighbours are creating, it is a problem the barbecuers are creating, and the latter is the one that needs to deal with it. Not a purifier for the naighbours, but no smoke and odours from you.
This is a nuisance, plain and simple. If they want to go down that route they can go to court and get an injunction against you. Swallow your pride and try to understand someone else's point of view.