Is saying gay alternative lifestyle politically correct?

No. "Alternate lifestyle" implies that it is a lifestyle chosen by a person, rather than an important and permanent aspect of who they are. It also implies a gay persons life is not normal. If anyone tells you that sexual orientation is a choice, set them straight (no pun intended).

Personally, I find calling it a lifestyle is offensive. I have a friend that has been living with me for years. Outside of the fact he is also a male, what is the difference between a straight persons lifestyle and mine? I go to work each morning. I eat three meals a day and look for companionship from someone I care about. How is that different then your lifestyle?