Yes, people should be granted asylum when they are persecuted for their sexual orientation. Sexual orientation is just a like eye color or skin tone, it cannot be changed so to persecute people for it is wrong. That is why I think those people should be given asylum to escape unjust laws and punishment for something they cannot change.
If we offer asylum to oppressed people, then we should of course offer asylum to those who are being oppressed for their sexual orientation. It is one of those areas that a lot of people do not talk about but it is a growing issue around the world because people are starting to speak up.
People should be granted asylum when they are persecuted for their sexual orientation. People should be allowed to leave their country if they are being persecuted for anything. Sexual orientation should become normal and people should not have to fear because of the people that they choose to date in society.
Asylum should not be expected from any country for any person. If the country agrees to asylum they are doing a favor for the individual. If a case came up where someone was persecuted for their sexual orientation and was in grave danger the country should have the right to allow asylum but it should not be expected.
The only reason I disagree here is logistical - in no way am I arguing that persecution of gays isn't a severe crime. The issue is logistical: assuming gays are present around the world in the same proportions as in the west (assuming 3%, the upper bound generally given to exclusively homosexual numbers in the population), this would mean the West taking in at least 100 million people.