It's a dependent clause, not a sentence. If you strike out "for", you have a sentence. The clauses "time and again" and "whenever policemen ..." are adverbial clauses that modify "delivered". If you strip away all the extras, what remains is "For the message is delivered" which is clearly not a sentence at all. It is only dependent clause.

In the context of the sentence you provided, the word "for" is used as a preposition. It is often used to indicate the purpose or intended recipient of an action. In this case, it is used to indicate the purpose or reason why the message is delivered. While the use of "for" in this sentence adds clarity and emphasis, it is not strictly necessary. The sentence could be rephrased without "for" as follows: "The same message is delivered, time and again, whenever policemen question gay-rights advocates (and sometimes their family members)." Both versions convey the same meaning, but the inclusion of "for" in the original sentence emphasizes the purpose or intended recipient of the message.