Most likely it is free will. But I agree with MagicAintReal on the claim that it is more complicated than this question asks. I am taking the position that homosexuality is not forced on a person by nature, and it is the same case for heterosexuality. Genes might play a part, but at the end of the day love and sexual attraction is subjective, so you are choosing.
Biological mutations are definitely not the case. There is no gay and straight gene. Like I said, your genes may play a part in your sexual orientation. But genes are no deciding factor, and genes are too complicated to dictate something as black and white as gender preferrence. Gender is a simple-minded concept, which makes it hard for it to correlate with reality.
From personal experience:
When I was a kid, I knew that some gay people existed but to the best of my knowledge, nobody I knew personally was gay. It was just something you heard about. In general, they were looked at as deviants, basically something to be looked down upon or ridiculed. Over time, with more and more famous people coming out or supporting gay people, I noticed that more and more people claimed to be LGBT. Today, it seams almost fashionable to be gay. They even coined a term for the fashion trend as metro-sexual. It seams to me that the more acceptable it is, the more likely a person will consider themselves as LGBT.
Evidence in a study done in 2012:
Some may claim that it is something people are born as and that the trend in more people who claim to be LGBT is because it is okay to admit it now. Seeing that it is just as okay for an older person to admit it today as a younger person, you would expect that they would be evenly distributed among people of various ages and about the same percent would admit to being LGBT among them. Problem is, this is not the case. In a poll of over 120,000 people of various ages over 18, they were all asked the question "Do you, personally, identify as lesbian, gay, bisexual, or transgender?" Here are the results.
Percent of those who said "Yes"
Notice how the percent doubled for ages 18-29. Clearly it is a result of how popular being gay has become. Because it has become more popular, it caused others to make the subconscious choice to identify themselves as LGBT.
Homosexuality could not be a mutation or an act of free will and this opinion poll neglects those options.
Why do people think that homosexuality is a mutation or some abnormality? Some people like canned beets (yuck) and some people like the same sex...Neither of these likes are abnormal or mutations.
This opinion poll is therefore bigoted and fallacious.
Human sexuality is very complex, and many different factors influence it. Cultural expectations, environmental factors, and genetics all play a part in it. The human genome is very complex. There are very few human traits that are governed by a single gene, so believing that we need to find the "gay gene" to prove that sexuality isn't a choice is ridiculous.
Multiple studies have shown there are distinct structural brain differences between straight men and homosexual men (homosexual men's brains are structured more like a woman's). Straight men are also better at tests involving spatial orientation and rotation than gay men and straight women. Vice versa, lesbian women perform better at these tasks than their straight counterparts. There are many other examples of differences that are beyond personal control.
No one really knows if there's one single "cause" of sexuality, but it's clear that it's not 100% by choice.
For a heterosexual, the thought of sleeping with a member of the same sex might be repulsive. For a gay person, the opposite might be true: the thought of sleeping with a woman might be repulsive. For some, neither is true, bisexuals don't care either way. Those are three options and each one has a preference they didn't chose any more than anybody 'chooses' how their personality is. It's not up to them.
My point would be this: Continuing to bring up this whole, "Is it a choice" thing is becoming increasingly more and more offensive. If you are fine with people loving whomever they want to love, like I am, then who cares either way? Really, does it matter in the slightest either way? If nature did it, they have zero choice. If their predilection for 'gayness' is just simply a product of nurture, how is that their choice? Either option is valid. If you truly support them, stop bringing this up.
Sexuality is definitely not by choice. Heck if it was choice, I would choose to be sexually attracted to people, but alas I am asexual. I don't think anybody would choose to be different and face discrimination and violence.
Sexuality is too complex to be a mutation. Studies have shown there are different genes in people that are not straight along with different levels of hormones. None of these have complete influence over sexuality as studies are still trying to prove that it also can be brain chemistry, hormones, certain genes on certain chromosomes that may be recessive, ect. But is it a mutation that suddenly came up? No, in fact homosexuality has existed since before Christ just like being trans.
I however do believe sexuality can be influenced by early stages of your life. Asexuality was not something I developed from sexual abuse as I've never been sexually abused, but it could be other factors in my early and critical growth stages that I don't remember. We may not know the "true cause" of being homo,bi,pan,ace, ect ever or we can know tomorrow.
I actually doubt that it could be influenced by both free will or genetics. With society, I doubt people would choose to be discriminated and hated with a decision that was punishable with prison or death. With science, there is no proof or correlation between genes and homosexuality. The field is still extremely new to call it an abnormal mutation. Human sexuality is influenced by your personality. It is not something that you can choose. I don't see anyone choosing to be straight. That's how they are. It's their preference. Some guys are bisexual. I say free will and genes dont determine who you're attracted to
A simple and short way to sum up my opinion would be:
Free will influenced by mutation and environment.
I need 31 more words, so just to clarify:
Because of my theological convictions: every person is responsible for their actions or lack thereof.
A homosexual has the ability to not act upon their desires the same way a heterosexual has.
Every person has genetic material that makes them prone to certain diseases, behavioral patterns, etc.
Combined with the proper environment, these mutations can trigger the prerendered behavior.
I believe people are born with their sexual preference and don't just decide it. But I wouldn't call homosexuality a biological mutation, it is a normal thing that has been oppressed because the social norm has for a long time been heterosexual. And lately people have started opening up and the social norm has also evolved so that all sexualities are now accepted.