This was "part of" western culture not 40-50 years ago. Societies evolve and open up to new ideas at different rates. That's never happening if you boycott them. If you held an election in Qatar on LGBTQ rights today, the results wouldn't change anything. That is to say, unless the people themselves feel a certain way you cannot force it upon them. And guess what will make people change the way they think?
Equating not boycotting the world cup to approving all LGBTQ abuse is just one of the many ridiculous things I've seen in the media. You have to look at the trajectory of a country and where it has come. Decades ago, for Qatari government to say all LGBTQ are welcome would have been insane. At the end of the day, boycotting the world cup achieves nothing for lgbtq but participating does.