I had a dog that was really over the top with a need for attention. He might. E fine for some, but I felt he was too. UCB in my face. At 70 plus pounds he was too much to handle. Plus his owner never licensed him and was a little flakey.
Is it possible to set my profile so that I am “hidden” from this client for future bookings?
No it's not.
To avoid a conversation, you can just message him - thanks for letting you watch Rover, you don't think you're the best match for him, and for future stays, you'd encourage him to contact Rover support at [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team], who will help find the perfect match at no additional fee.
I try to be straightforward with owners. If a dog is too high-energy or requires additional handling, I'd make it clear in a polite/honest way. "Thank you for booking me, but I may not be the best fit for Rover for future visits because I don't have a yard for him to burn off extra energy, it's difficult for me to handle him due to his size, etc." I'd also update your size preferences/profile if this is something that could apply to similar dogs (it may just be this particular dog, though).