If you look at it historically, gays had been severely pathologized in British society (and of course, in others) - by the law, by medicine, psychiatry, religion, and so on. However, there has been a counter-movement, so that homosexuality was decriminalized in the UK, and then marriage was equalized, medical attempts to 'convert' gays were banned and so on.
This counter-movement has made great progress in different areas, so that for example, few doctors today would see gays as pathological, or in fact, psychiatrists also. Religion seems to be a backwater, for various reasons. So anyone who supports the acceptance of gays will tend to criticize the C of E and Catholic Churches for their official homophobia.
And of course, there are Christians who do criticize the churches and any homophobic Christians.