It's somewhat contradictory that these positions both come from the same person.
Firstly, the comparison between being religious and being in the kkk wasn't what was being said. It was comparing homophobic bigotry being compared with racist bigotry (albeit both being masked by religion - this woman claiming religion as the basis of her homophobic bigotry, and the kkk using religion as the basis for their racist bigotry.
Essentially the point being made was "would you defend someone who refused to do the job they have chosen to do, in line with their employer's practices and policies, simply on the basis of the skin colour of their customer in the way you are defending this woman refusing to do her job on the basis of her customer's gender/sexuality?" (or arguing against the punishments given)
If anyone on this thread is making a poor comparison, it is you.
Your comparison of this woman to gay people being imprisoned is flawed. They were being imprisoned because they were gay. They didn't chose to be gay. Being gay wasn't a belief that stopped them doing their job as instructed by the courts. Whether the excuse given by courts were that they were imprisoned for who they were born, or the acts (that are part of being who they were born) that they did doesn't matter. It was still about who they were.
This woman has not been imprisoned simply for being who she was born to be, but about the choices she makes despite options that have zero impact on her ability to be who she was born, or her chosen religious beliefs.
