For many groups the point is that the group defines its terms, or rules of engagement. So if you want, for instance, to restrict membership to people who live locally, or who have a high IQ, or who can speak Italian that’s ok. MENSA, the Hometown Garden Society and the Advanced Italian Conversation Group can only exist under those circumstances. As Galaxy says, it is a clash of rights.
I think it is wrong of the C of E to refuse to marry gay people, but if all religions had to behave in the same way they would cease to exist. I suspect that Justin Welby would personally like to be able to marry gay couples too, but I understand why he can’t order his priests to do so.
It will come in time, I think, and great strides have been made over the past 20 years. Cold comfort to those who want to consecrate their love now, of course, but unfortunately for them, a group who exists because of a belief system can’t be forced to alter those beliefs or they would no longer be the group they were.