I'd suggest that since you have some deal breakers listed under Before You Contact me, that you may want to use the Rover messaging system to ensure the dogs scheduled for a meet & greet are a potential fit, because not every pet-parent reads all profiles before requesting a meeting.
Since some meet & greets may not result in a booking (it's possible their plans change, family/friend cares for pet instead, or they book a different sitter), I would not hold off a meet&greet with the second requester, especially since some meet & greets are set far out. Certainly, you could let them know you will be meeting with someone else for those dates and you could let the first requester know that others are also interested in the same dates.
Until it's booked, you're not obligated to hold a space for them.