It depends on how you define the world 'normal'...it is a very vague word.
There is an incredibly broad range of human sexual activity. Just because 80% of people fall in the 'average' range of what they all actually do sexually does not mean that those outside of the 80% are not 'normal'. If 80% of people routinely use four different sexual positions in their sexual behavior, is the individual who uses eight 'abnormal'?
If one accepts that being gay, lesbian, or transgendered is not chosen, but a given of genetics, then are we to say that there was somehow a 'mistake' made by the Creator and these people are 'abnormal' and should never have sex? Is the Creator that stupid or cruel? I think not. Look at the diversity of the world. The Creator delights in it.
Is homosexuality normal? Absolutely. Average? No.