What might it look like if someone wanted to treat Christians the way gay people are treated?

For one, tax benefits afforded to other not-for-profit institutions would be denied to churches, probably on the basis of separation of church and state. There are some who advocate for this, but they are not GLBT groups.

Christianity would be portrayed as a form of mental illness to be cured. There are some who advocate for this, but they are not GLBT groups.

When children gave their lives to Christ, their parents could have them shipped off to programs where they would be taught how not to be Christian, showing tough love for these wayward youth. There may be some who advocate for this, but they are not GLBT groups.

There would be programs to help people struggling with Christianity by using aversion and (probably in the 50's or 60's) shock therapy. I don't think that ever happened to Christians.

Christianity would be seen as a reason to deny custody - and even visitation in some cases - of children to a parent.  There may be some who advocate for this, but they are not GLBT groups.

Christians would not be allowed to adopt - or even be foster parents - for fear of indoctrinating children in the ways of Christianity.  There may be some who advocate for this, but they are not GLBT groups.

Christians would not be allowed to teach for fear of indoctrinating children in the ways of Christianity.  There may be some who advocate for this, but they are not GLBT groups.

Students would not be allowed to have Christian groups, or Christian-Atheist Alliance groups, probably on the basis of separation of church and state. There are some who advocate for this, but they are not GLBT groups.

Clergy would not be allowed to visit patients in the hospital, as they have no legal relationship with the patients. I don't know of anyone who advocates for this.

The behavior of a few Christians would be held up as "how Christians act". Some GLBT people do that in the context of how Christians treat them. But it would go much further: examples of beliefs in young Earth creation, the church's historical opposition to cosmology that wasn't geocentric, the bloodiness of the Crusades and the cruelty of the Inquisition, and the deaths of children refused medical attention or having the demons beat out of them based on faith. There are some who regularly portray all Christians this way, but they are not GLBT groups.

There are some who treat Christians the way some many visible Christians treat GLBT people.  But those some are mostly not GLBT people, and there is no organized GLBT effort to do to Christians what organized Christian efforts do to GLBT people.