@Marilyn157 Yes, on an Inquiry you can safely ignore those messages. They are worded so as to make hosts think they have do one of those things, but that's just because Airbnb's goal is to get bookings and collect guest fees.
A Booking Request is different- you do actually have to either Accept or Decline within 24 hours or get dinged on your response and acceptance rate. But you can still message back and forth with the guests before you do that, as long as you click on one of those options before the clock runs out. If the guest is asking for things you don't provide, or indicating they want to bring their dog, when you have a no pets listing, you can message in such a way so as to encourage the guest to withdraw the request before 24 hours so you don't have to decline. You can mention to them that if they don't withdraw the request, as hosts get penalized for declining, if they don't withdraw it, you'll have to Accept, but only on the condition that they don't bring their dog. And that if they don't withdraw it and you Accept, their credit card will be instantly charged by Airbnb.
"Hi XX, Sorry, but I have a no pets listing, which I don't make exceptions on, so won't be able to accommodate your dog. I wish you luck in finding a pet-friendly listing. I encourage you to withdraw this request ASAP, so you don't get charged by Airbnb for a booking that doesn't meet your needs, which would mean you'd then have to cancel and wait for a refund"