My 2 cents:
I lived in B'ham for 5 years. And had to visit, until recently, with my last job. At the time I could not carry, due to living on a college campus (where it was located, I sure wanted to...) and working in a job where it was forbidden. My experiences with the local PD were generally unfriendly. They seemed to not be well informed of the law, seem to have little training, and some seem to have authority issues. This said, not all are like this, several work hard to do it right, and in several cases, the City is at fault for not ensuring the PD is well paid, and well trained. To see how messed up the B'ham Police Dept is, merely drive a few blocks down towards I-65 from their downtown headquarters (1st Ave)... See the drug, prostitute, and crime trade occurring within sight distance of the HQ, and you understand there is a lot of issues in Birmingham...
Seems you had an encounter where the police were already amped up, due to responding to a fight. Seems you handled yourself well, and were polite. Keep being polite, and firm. Change is a slow animal.