What is the southernmost capital city in the united states

In the continental US= Austin, Texas

Overall US= Honolulu, Hawaii

Explanation:

Although Florida is the southernmost state in the continental U.S., and home to the southernmost point in the contiguous 48 states, its capital of Tallahassee is just ever-so-slightly north of another state capital. Austin, Texas, sits at 30°16'2" N, a fraction of a degree south of Tallahassee, which is located at 30°27'18" N. That makes Austin the southernmost state capital in the continental U.S. — but not, it should be noted, the southernmost state capital overall. That title goes to Hawaii's Honolulu, which has a latitude of 21°18'25" N but is not included in the continental U.S.

separation of church and state? not sure what you mean.