@Ciara143
Ciara, there may be a genuine reason why a local booked guest would want to view your property before the scheduled stay. There may be a disability involved and they need to assess the suitability of your listing. Their own property may be undergoing renovations and they want to get an idea of facilities they need close to you. But there is an overwhelming body of evidence that guests who go down this path will use any such visit to their advantage.
1/......They will gain enough information to cancel the Airbnb booking and attempt to book with you direct in an attempt to get a better nightly rate.
2/......They will see something that is not to their liking and cancel the reservation and look elsewhere.
3/......As they are locals they are sizing up your properties suitability to hold a party/function of some sort.
Ciara guests fall into two camps, they either like what they see and just want to stay, or they want to take advantage of you and haggle about what you offer. Hagglers never make good guests and in your situation I would get onto Airbnb and tell CS this guests is asking for conditions contrary to Airbnb's rules and tell them you don't feel comfortable proceeding with the reservation!
I would not take the risk, just from your description they sound pushy, I would stay well clear!
Cheers.......Rob