It is as relates to compelling someone to create custom content on your behalf, to express your views.

I can't use a religious belief to refuse a rote service, but I can to refuse bespoke work that expresses your views.

This case was never about refusing service to LGBT couples, it was about refusing bespoke work. To paint it as anything else, and in defense of your argument that "Conservatives are anti-LGBT" because of this case is wrong and nothing short of propaganda.