Do they allow thong bottoms?

Yes

https://dnr.maryland.gov/publiclands/Documents/SandyPointFAQs.pdf

No they dont alliw thong bottoms

I don't know whether there's a rule against them, but whenever we've gone to this beach it's been mostly families with younger children. We've never even seen alcohol there. Thong bottoms could be awkward for that environment, probably for others AND the wearer. :) I'd say try it after sunset when there's an older crowd, but the beach closed at 8pm when we were there 2 weeks ago.