You're collapsing a huge societal design space into a narrow, ultra-individualistic western viewpoint. Your point only makes sense in societies that take it as a given that individual autonomy trumps the right of society to enforce behavioral, moral, and social norms. That approach is not morally required and almost no non-western society embraces that viewpoint. Almost all of Asia and Africa accepts that requiring conformity in
voluntary lifestyle and personal expression is legitimate. There is nothing special about sexuality in that respect--nearly everyone in the world thinks its perfectly legitimate for societies to, for example, impose taboos on sexual activity outside the bounds of some marriage-like relationship. By your reasoning, modern western sexual permissiveness is morally required--even when it comes to voluntary choices. That's a radical (and quite ethnocentric) claim.
In that context, whether something is a choice, versus a characteristic that cannot easily be changed, is tremendously important. It elevates the issue from ordinary policing of norms into the realm of human rights.
And of course, it's ridiculous to say that people "latched on" to sexual orientation being immutable to appease "bigots." Sexuality being immutable (or at least not easily changed) is an observation that rests on the experience of countless individuals who suffered tremendous pain and suffering trying to deny their sexual orientation. And the article, of course, nowhere suggests that sexual orientation is a choice. Many things are immutable characteristics, or at least not easily changeable--without being traceable to a specific gene.