As bad as this is, it isn't quite as bad as you paint the picture, for several reasons.
First of all, there really isn't any "right" to marriage, even for heterosexuals. Since an inalienable right includes an obligation on all other human beings to honor that right, you can see that this particular "right" - along with all the other socialist "rights" - is no right at all. While I may very well have the "right" to marry the woman of my choice, there is no woman anywhere in the world who is obligated to marry me.
Secondly, churches are voluntary associations of like-minded people, which both accept new members and remove old members all the time, and for their own reasons. In this country you have the right to worship as you wish, but no church is obligated to accept you as a member of its association, nor can it keep you in membership if you choose to leave, for that matter.
And therefore, a "right" to marriage is not at the same time a "right" to a church wedding, since civil authority in all jurisdictions also conducts wedding ceremonies.
Granted, all these points may be contested in various courts of law, and in some jurisdictions with courts which disregard the US Constitution as a matter of course, the church may "lose". Should that come to pass, however, I predict that those churches which are against homosexual marriages (and there are many more of them than there are for such nonsense) will simply disband and re-form at a later date. If the homosexual lobby wants to waste its money in such a never-ending spiral of fruitless (no pun intended) lawsuits, they're not only venal and corrupt, they're stupid.
I hope and pray that you are right about that. The Episcopal church is learning about this, and the orthodox are in the process of disbanding. However, the topic is important and will take vigilance from all church members. There are other denominations that are likely to be facing the same issues soon.