Homophobic is an over used term tbh; more often it seems that we should be using homonegativist or some version of the term beginning with 'miso' (though the phrasing then becomes awkward such as misohomosexualist not a word btw) rather than fear it seems to be about disgust or hatred at some level not necessarily of the people but rather of either the people, the inclination or the act; we should not be so quick as to assume it is a phobia... though I do understand that is far more pleasant and less judgmental to use that term than to name it for what it often is - simple bigotry which is far worse than a phobia and we should avoid using the term as a result.
For the record I recognize that I am slightly homophobic (though believe I mitigate any manifestations of this quite well), that said, the idea of the 'gay agenda' ('rainbow mafia' and all that jazz) is a nonsensical concept. Instead the most that could reliably be said, would be that many people in the LBGT community might be inclined to encourage a tolerant mindset. I.e. people have their differences, provided everyone directly involved has given informed consent, there is no problem and you should mind your own business. Many within the LBGT community might also hope to encourage not merely tolerance but acceptance... given the extreme lack of tolerance in many portions of society however, they are probably better off facing one hurdle at a time, attempting to foster tolerance at a personal level and at the level of institutions both public and private; some people and some institutions are less tolerant than others - a sad but inescapable fact.