Because it an abuse of individual liberty and conscience and is a longer camel's nose under the tent of government sponsored enforcement by law for it's favored groups - not to mention it is a direct infringement on our 1st Amendment rights which are not merely "civil rights", but God-given rights enshrined and partially enumerated under our Constitution.
There is a huge difference between the widespread government Jim Crow laws of the Old South (which were designed to prevent the free exercise of rights and liberties of a minority) and the current demands for more laws and enforcement to favor certain favored groups and abridge the rights of genuine liberty and conscience - particularly religious conscience.
Taking it a step further, if the government can so easily abridge individual religious and moral sensibilities on those not supporting homosexual behavior (a learned sinful behavior and not an immutable human characteristic), then what is to prevent (for example) the government and favored groups from requiring doctors and nurses to perform abortions or euthanasia against their will? After all, being these livelihoods require government licensing and are money-making businesses. Or what is to prevent them requiring pastors/priests perform homosexual marriages and publicly "celebrate" this and other abhorrent life-styles? After all, churches enjoy tax-exempt status and other legal privileges? Use your imagination. The list is endless.
This is a slippery slope and one Liberals plan to use to remake America into their own twisted image and moral vision for their own goals. It is not one based on anything resembling Christian conscience and morality and it is contrary to a free people and society which our Founding Fathers envisioned.
I would like to quote you in a column I’m writing. Let me know if you object.
Your mention of requiring doctors to perform abortions, reminded me of a move by some medical schools to require students to perform an abortion (so they’d know how) as a condition of graduation. I’m not sure how that was ever resolved, but it is definitely revolting.
The extent to which government will go to wipe out any sense of individual moral choices is astonishing.