So, don’t say “I have no problem with gay people” because it makes you look like a hypocrite to them. They think that if you have no problem with them, you won’t have a problem with their homosexuality, because they personally identify with it, and don’t separate it like you do. So it’s unhelpful to allow them to conveniently write you off as a doublespeaking bigot.
Let's put it the other way. There are some who will say that they have no problem with Christians, or that they value the First Amendment, but then turn and say that they don't think Christian faith and doctrine should influence government policy, and that "you can believe whatever you like, as long as you keep it to yourself." This is essentially the same experience that homosexuals have had with others telling them to "stay in the closet" and hide a part of who they are out of shame.
Why would we treat others the way we don't want to be treated? This is the opposite of the Golden Rule, which is that we should treat others the way we DO want to be treated, even if we are not treated that way. The fairness toward others is a witnessing tool. When people realize you're treating them kindly and that you're not obligated to (or even that they're not deserving of it), they are more apt to listen to you.
But saying that you don't have a problem with gay people is not a kindness. It is confusion. True kindness would be to say in unequivocal terms, "I believe homosexuality is a sin, but I do not hate you for who you are. Instead, I love you in spite of who you are, because that was what Jesus Christ did for me." Then go on to say that because you believe it's wrong, it would be unloving to encourage someone to do or be proud of what is wrong and harmful for them. True love shows itself in correction. When you demonstrate that you love them to the point of being hated and harassed for pleadingly showing them the way to be saved, you give the Holy Spirit an avenue to open their hearts to the Gospel. They'll see that you're not motivated by love of self but that you sincerely care. And some will still reject you. But at least they will not do so because you were an offense, but because the Gospel is what offended them.
~ Rak Chazak