There is no liberty interest in the homosexual "marriage" movement.
I heartily agree with all of the above.
It is an authoritarian position, dedicated to using the police power of the state to force others to act against their moral or pragmatic beliefs about certain kinds of behavior.
Who exactly is forced to act how exactly?
Catering halls, photographers, insurers, adoption agencies, churches, publishers, etc...
Some of the episodes so far involve businesses' being sued to provide services to declared homosexuals, when the business owners don't wish to. Charitable organizations have been forced to stop facilitating adoptions because they will not place children with homosexuals. Government schools in some states now insist children be taught that homosexual behavior is positive in every way.
I'm unable to determine whether you are deliberately being disingenuous in your questions. These topics have been covered in depth for several years on FR, with examples from a number of U.S. states as well as foreign countries.