Its not data specifically about restaurants but there's lots and lots of data available from things like caravan sites, air bnb, booking.com and holiday cottage sites of the millions of dog bookings and high percentages of bookings on each including dogs.
A huge portion of those won't allow people to leave their dogs in the tent/cottage so if you want those people to eat in then yes you will need to allow them to bring dogs.
I worked in a dog friendly restaurant and know my area is famous for dog friendly beaches, and having lots of camping etc so yes it makes sense locally to us not to exclude a big portion of tourism trade.
Again
The biggest portion are probably ambivalent. These people could go absolutely anywhere including big chain competitors which are cheaper
There's a portion that want to bring their dogs. These people have a much more limited choice so can be good to capture
A portion that would prefer dog free but will come any way.
And a portion that will boycott. It depends on how well served this market is. Locally this market still has sufficient choice that an extra dog free cafe is likely to not benefit from them as much, and be surviving on the ambivalent
I have dogs and obviously visit a big selection of non dog restaurants but that's often in a planned way, so if you are somewhere relying on passing trade then its dangerous to send customers back home and hope they come back.
Its also sometimes a seasonal thing. In the half terms, summer holidays there is a noticeable boost of tourists without dogs where you could probably easily survive. However in term times, out of the sunny periods its noticeable that its dog people that come back again, and that if you want to stay open in tourist areas in the wet and wind then you'll find its people with dogs who are still caravaning, out walking etc