Airbnb probably disabled their account due to lack of verification or concerns such as the ones you already noted.
When someone inquires or reserves your listing, you may ask their full name and where they live and look them up on social media or Google them to do your own verification.
If they seem suspect they probably are suspect.
Guests who are going to be good guests are very communicative about themselves, their companions, their travel plans, their identity and their excitement at meeting you, their host.
If they seem weird and reclusive, they will likely be weird and reclusive. If they won't give you their full name and where they live (city and state or country, not their personal address) then you can and should decline them.
You can also review the verifications they have on the site and if they are not to your liking you can ask them to provide more. You can require a good photo and decline them if they provide a picture of a potted plant. However, many reasonable people do not use their personal photo (like me:) for various reasons.
Be wary of locals trying to get a place to stay. They are often in dire personal straits or have been evicted, or plan to party, or get high, or even die in your home. I have had two different friends recently allow pathetic homeless aquaintances to stay with them (not through Airbnb and not their close friends) and had the person die while staying, one from a heroin overdose and one from a massive heart attack and bleeding out (on blood thinners?) in the guest bedroom!
I recently allowed a pathetic homeless acquaintance (friend of my friend's daughter) to stay two nights in my listing but decided to evict her on the third day after she was arrested for shoplifting a few minutes before I was supposed to pick her up in town to bring her back to stay another night. Long story, no good deed goes unpunished . . .
City Limits Ranch