It's not about hating anyone or anything; it's about removing people's and institutions' ability to act in discriminatory ways that are against the law. If being discriminatory is a conscience thing, well OK (maybe!), but it shouldn't be allowed in public spheres. Since the C of E is a 'state' church, it's public and needs to accept that what the majority of the public wants in a democratic society is what it should get.
I accept that that is probably not a watertight argument, but it just needs a few bungs andnit will be.