Two versions of the interaction with the centurion have been posted. One refers to the ill one as his servant and the other refers to the ill one as his son. The billboard does not claim that Jesus was gay, so it must mean that the centurion and the ill person were a gay couple. So the billboard is saying that the centurion was having homosexual relations with his son (i.e. he is a child molester) or with his slave (probably non-consensual). Neither makes gay couples look real good. They probably need to rethink their PR on this one.The idiot who put up the original billboard is ignorant of history. Homosexuality was actually quite taboo in the the Roman Republic and early empire period, and it was "officially" frowned upon in the legions (though some activity doubtless occurred).
Some Romans who were of the homo persuasion perversion would spend a lot of time on "business" in Athens so they could find all the bum-boys they wanted.
The Greek word used in Matt. 8.6, 8.8, and 8.13 is
pais which means "child" in relation to descent (either "son" or "daughter" but here it is used with the masculine article), also used of a child in relation to age, or of a servant or slave (regardless of age).
Here the meaning "slave" is obvious from the context--if the centurion was speaking of his own son he would have used the word for "son" (hyios).
Greek pederasts also used the word pais of their boy "lover" but that is clearly not the usage here.
Jerome's Latin translation uses the word puer which has the same ambiguity ("boy" or "servant").