People tend to have all their logical fallacies and one of them is, "If you don't support something, you hate the people involved in it!" That's not necessarily true because there are outcomes to why you don't support something. If a decent parent doesn't support the idea of their children getting involved in stuff like posing for indecent pictorials, working for sleaze clubs, fraternities or drug dealing - it's because they love their children. If parents refuse to give their child whatever won't be good for them even if they want it - it's because they love their children. The same goes to why Christians go against something because they love people.
As the Christian grows, the Holy Spirit makes them grow in love. Christians are willing to stick their neck out even if it means suffering just to get people the truth of the Gospel of Jesus Christ. Just because they're against other religions doesn't mean that they hate the people practicing that religion. Many people today play the victim when they're told the truth about their religion and/or sinfulness. The truth is there's always that statement, "You can tell the truth without love but you can't have love without telling the truth."
1 Corinthians 13:6 says that love doesn't rejoice with iniquity but in the truth. Do you know why Christians are willing to risk themselves to tell the horrible truth about man's total depravity and that Jesus is the only Savior from sin? It's not because they hate people. They love people enough to tell them the truth about their lost state and that they need Jesus Christ as their Lord and Savior. They don't want people to land in Hell when they die. They hate what sends people to Hell and love people enough to tell them the truth!
The great evidence Christians love the sinners while hating the sin is that they may even be willing to accept affliction, suffering and death just so the person will hear the Gospel of Jesus Christ? Because Jesus died for the sins of man and chose to do the will of His Father than the easy way, think of what Christianity has been. Many Christians were brutally tortured in every way possible like Stephen the first martyr recorded in the Book of Acts prayed for his executioners. Aside from boldly facing death but the fact they would publicly pray for their enemies has only caused Christianity to increase in its ranks. Many spectators may have seen, "Look, how different the Christians are! I want what they've got!" That shows that Christians are willing to die for the lost sinner showing how much that they hate sin but love the sinner enough to tell them the truth.