I am glad to see your search is bringing you to belief in the Church. I am sorry you are experiencing discouragement. I know I have been blessed to always live in places where there are multiple Catholic parishes close by and they’ve all been pretty solid (though not without problems, of course).
I would still advise keeping an open mind and extending the benefit of the doubt. I grew up Catholic, but experienced a strong recommitment to my faith in college. When that happened, I went through a period where I felt like my eyes had finally been opened and I started to see things in parishes that I didn’t like and thought were wrong. Anytime I went somewhere new for Mass, I’d find myself evaluating whether or not the priest was wearing the amice to cover his collar, whether the candles were wax or oil, and a whole host of other “abuses” I was constantly on guard for. Frankly, it was exhausting. And I came to see that in many cases, I wasn’t even correct over what I thought was an “abuse.”
The devil wants to do whatever he can to steal our peace and drive a wedge between us and Christ and the Church. I think a common trick he plays—particularly on those who are starting to take the faith more seriously—is to get us to be constantly suspicious of our priests and fellow Catholics. Then we find that we go to Mass and spend more time in fear and discouragement than we do actually entering into the Paschal Mystery and focusing on God.
We are far better off if we presume good will rather than ill will. Right now, all you have to go off of is a tiny blurb on the parish website. Sure, it’s possible that your priest does not agree with Catholic teaching on the immorality of same sex activity. But that is not the only possibility. It is also reasonably possible that he has made the judgment call to reach out to a group of Catholics who are often disenfranchised not because he wants to confirm them in any sin they may (or may not) be committing, but because he wants to draw them closer to Christ. So given the choice between the two, we would do better to presume the latter rather than the former.
Certainly you can ask for clarification. But then you have to decide what you will do. If your worst fears are confirmed, is it worth leaving the Church because your pastor has a few theologically suspect opinions? As Peter said to Jesus when asked if the apostles would leave, “Lord, to who else shall we go?”