In general, in nearly all US jurisdictions, a strip search is considered reasonable only after the person is arrested, and this is specified in most local, state, and other laws, and/or in detention facility rules and procedures.
The usual requirements of "probable cause" for an arrest would apply, but that's a somewhat different matter than whether the search was justified.
In this case, the police had a warrant for arrest for the person involved and he was arrested, based on that warrant, before the search took place.
The comment in several articles on the SCOTUS decision that "not paying a fine isn't a crime" in the place where it all happened is meaningless, since no warrant can be (legally) issued without approval of a judge who finds that probable cause for an arrest exists. Since they had a warrant in hand, the police had no real choice about placing him under arrest. His claim that he "had proof" that the warrant was unjustified is immaterial, since the cops don't hold court in the street.
He could possibly sue for false arrest, although there's probably little real chance of finding someone "responsible" in this case to sue. Since he was "under arrest" at the time, he can't make much of a case over being treated the same as others who are arrested. If the treatment of those arrested is consistent, it's up to the legislatures (and/or chiefs and wardens) to make any needed reforms in how prisoners are handled.
(Others may be more sensitive over this, but being old and ugly I don't much care who looks at what I've got. It's their problem more than mine. Some people might have more cause for shyness, and I think I can understand some cases where it might be a concern.)