One argument (or assertion) which homosexual activists use is that Christians have no right to "impose" their views on others. Religious beliefs have no place in law and public policy. However, that argument is wrong on several counts:
i) It commits the genetic fallacy. The source of an idea doesn't automatically discreit the idea. You must consider an idea on the merits.
The question at issue isn't whether beliefs are religious or secular, but true or false.
ii) Of course, an unreliable source might make it unlikely that a derived belief is true. That, however, is a different argument. It's not just that the belief is religious, but the further claim that if a belief has a religious source, then that's an unreliable source. That renders the belief ipso facto suspect.
However, if that's the argument, then the proponent of that argument assumes a burden of proof. He must demonstrate that, by definition, religious beliefs are unjustified or false. He's making a claim about religion. In the nature of the case, religious beliefs are dubious. But there's an onus on him to prove that contention.
And, of course, Christians have argued, from various lines of evidence, that Christianity is true. It's not just a matter of faith, but reason.
It's not as if there's a standing presumption that Christian ethics is false. A case has been made for Christian ethics by Christian philosophers and apologists.
iii) In addition, we have a representative form of gov't. Christians are voters. They elect lawmakers to represent their views and interests. Under our system of gov't, citizens have the political right to promulgate laws which reflect their ethical views.
That's majority rule. The consent of the governed.
Majorities elect the winners. The winners pass laws that, in principle, reflect the will of their constituents. The people who elected them in the first place. If they are perceived as bucking the will of their constituents, they may lose their reelection bid.
The only restriction is if that violates the Bill of Rights. The only Constitutional restriction on religion is the prohibition against religious oaths for officeholders and the establishment of a national church.
Conversely, the Constitution explicitly protects the free exercise of religion. Well, that can be expressed at the ballot box.
iv) Even if, for the sake of argument, you think religious beliefs are false, that doesn't invalidate laws informed by religious beliefs.
Voters can elect a candidate based on misinformation. The fact that they were motivated by erroneous beliefs doesn't nullify the election. The winner is still a duly elected official. He was elected by a legal process.
Likewise, even if you think a law is based on misinformation, that doesn't invalidate the law. Right or wrong, it still has the force of law–unless and until it is repealed.
A mistaken law is still a law. Many people thought Prohibition was a mistake. But it remained the law of the land until it was finally repealed.
Suppose a candidate convinced voters that aliens from outer space pose an existential threat to human survival. We need orbital weapons to repel an alien invasion fleet. Suppose he's elected on that platform.
Even if that's nonsense, a voter's false belief, which motivates him to cast his vote for that candidate, doesn't nullify the election.
If voters pass a referendum, based on their misunderstanding of the issue, the referendum doesn't cease to be legally binding. A voter's motivations are irrelevant to whether he cast a legal vote. He may be a fool. He may vote for foolish reasons. But his reasons are irrelevant to the legality of the process. That's not the criterion. We don't screen voters that way.
From a Christian perspective, atheists are irrational. Votes cast by atheists are intellectually suspect. So the objection cuts both ways.