There is no overcoming being an introvert. That is if this guy is really an introvert.
The word introvert is thrown around and misused so often that few people know a real introvert when they see one. Similar to the letters OCD - people abuse this term as well, thus real OCD personalities get no real recognition.
Assuming for a moment he really is an
introvert Then he is going to need to set realistic goals and limits to his social activities and accept that he is an introvert and no amount of 'trying' is going to make him an extrovert.
Assuming you are a fag-hag or what I call a 'gal-pal' chances are high that you hold the magic key to get him knocked up, Erm I mean hooked up. In decades past it was my own gal-pal that dragged me to social (gay) events and was there to support me through everything as a 'gal-pal' which lead to a few interesting meet-ups with guys.
As for his picking up on 'straight' guys. That isn't a broken gay-dar. That is just too much isolation and insufficient time around human beings to become a bit more perceptive of how humans scream their alignment, sexual orientation and other things through body language, facial ques and other minor tell-tale signs.
Also he might not be around sufficient number of gay men. Hang around straights all the time and all you will find is straight men.
The number one problem with Virge, pardon I meant "the world" is that everyone wants to force introverts to be extroverts and cannot or will not accept that an introvert is what they are and cannot change. No one demands the extroverts to sit down and shut the fuck up and stop pushing into every nook and cranny of society, no one would dream of suggesting that and extrovert changes to meet the needs of another group, yet it happens to introverts all the time.
What that ends up doing is pushing introverts to 'try' and change and to force themselves into situations where they blunder, make mistakes or end up using substances and crutches in order to go from 'shy' to life of the party.
Perhaps your friend's real problem is there are too many people around him telling him 'He Should ___________' (fill in the blank) instead of allowing him to be himself and do as he is?
If he feels pressured into getting hooked up, into getting into the party scene and all of that, its going to lead to one mistake after another, and open him up for various levels of harm, not only harm from untrustworthy people, but self harm as he combats his real desire to be alone and turns to things like drugs, alcohol and other stuff in order to be that which he isn't.
Introversion is a very real behavioral pattern, a real character type. It is not a disorder, it is not 'sickness' or 'wrong' it is what that person is. He needs to accept what is, and learn how to cope and work with it in day to day life. Most importantly, those few people he will keep around him (as introverts have few friends, but the friends they have will be cherished far more than by others), need to accept him as he is and stop that incessant pushing him to be something he is not.
Eventually the right man will walk into his life. He just has to be patient.
I'm an introvert and have been in 6 relationships, all of which just happened on their own, pretty much when I least expected it to happen. I didn't need someone to shove me into the arms of another.