The Bible calls us blessed if we are falsely accused for Jesus' name sake (Matt 5:11) and He gives the clear impression that being misunderstood is simply part of what we should expect when we bear the name Christian. In fact Peter even describes it as our calling as witnesses of Christ to bless those who speak and do evil against us.
It seems one of the great falsehoods of our age is the popular accusation that Christians bigoted or homophobic because we think of various culturally-popular ideas are among the many ideas the bible calls sinful. But as you know, this actually reveals a profound lack of knowledge and an unwillingness to understand the Christian faith more than anything else. The most central idea of Christianity is that God only saves sinners, even the worst kind like me ... and those who continue to have high thoughts of themselves or their own goodness have no hope for being made right with God. But all who, by the grace of God, repent of their self-righteousness and trust in Jesus alone, whatever their sins may be been, will be given a new heart, will be reconciled to God, know the forgiveness of sins and be granted eternal life.
It is one thing for people to disagree, to say they disbelieve Christianity and that their beliefs differ from ours, but quite another to pull out the prejudice and bigotry card falsely painting an evil motive on the Christian's call to help liberate fellow sinners from captivity. But we are called to "bless" those who make false accusations ... and since this seems to currently be front and center in this age, we ought to commit it to prayer how we can best bless the culture around us even when they accuse and falsely represent. How we can do good to all who are created in the image of God.
May the Lord give us wisdom to be humble and yet persevere in his ways.