I always host M&Gs at my home, unless the client requests otherwise. One of the realities of running a business out of your home is that your home also doubles as a work environment, and just like you'd never send your dog to a daycare or kennel that didn't allow you to see their facilities, a lot of people would never leave their dog with a home sitter who won't allow them to see their home.
If it helps, I structure my M&Gs so the owners come to my home, but I meet them outside on the sidewalk first to meet them and their dog(s). Then I bring my dogs outside for introductions, and we take them all for a walk around the neighborhood. This gives us time to get acquainted and let the dogs calm down before going inside. It's never happened, but if I were concerned about letting them in my home, I could end the M&G before that happened. In our discussions I let the owners know this will be the plan. I'd also encourage you, if you're concerned about a client coming by, to have a friend there with you for the M&G, or at least let someone know who will be by and when and have them check in with you after a designated amount of time. Or, instead of giving owners your address, give them the address of a nearby park or coffee shop, then after intros are done, invite them back to your home to see where their dog will be staying. Not all owners will be concerned about seeing your home (though in my experience most will be), but if you refuse until after booking the stay, you may lose a lot of great clients.