It’s no surprise that both Cook and whoever wrote this focus on ‘identity’. Because applying the word ‘identity’ to sexual attraction serves to muddy the issue, and that is precisely what these people want.
‘Gay’ is an adjective applicable to someone who finds members of their own gender sexually attractive. To say “I am gay” is simply stating something about oneself. It could only be an ‘identity’ if you constructed your whole persona around it (which admittedly some people do but they are rather sad). Do you fancy people of your own gender? You’re gay, that’s what ‘gay’ means, and if you don’t like the word ‘gay’, then tough. You can use alternative words or not talk about it at all, the option is there, but the word ‘gay’ will still be applicable to you whether you like it or not.
Now, as for Christians… in particular the ones who think they’ve become ‘new creatures’ after they convert, which is specifically the ones this article refers to… that includes them. Unless they have actually changed their sexuality (very doubtful) or have actually lost their sexuality in some way (which is not uncommon and is rarely connected with Christianity) they’re still going to be attracted to their own gender. Doesn’t matter if they suddenly think it’s an appalling sin. Doesn’t matter if they’re doing their damnedest not to. Doesn’t matter if they hang on every word of the Bible. Doesn’t matter if no-one ever talks about it. The word ‘gay’ still applies.
And Becket Cook is gay. He does not construct his whole persona around it. He does, however, construct it partly at least around being ‘ex-gay’. Which makes him very sad (as opposed to being ‘rather’ sad).