You can always say the truth without loving but you can never love without saying the truth. One says the truth to hurt or offend or one can say the truth out of concern. Let's take the example of the loving parent who tells the truth to the child why they aren't allowed to "fit in" with the popular children in school. The parent lovingly tells the child the truth that to become like the popular children is to wreck one's future. The loving parent refuses to spoil the child rotten not of hate but out of love. He or she doesn't want the child to grow up as self-centered but God-centered. That's real love over a child who spoils the child rotten, Proverbs 13:24 warns, "He that spareth his rod hateth his son: but he that loveth him chasteneth him betimes." If you don't discipline your children then you really don't love them. You really hate them without knowing it. If you loved them then you wouldn't do anything to them that will ruin their future.
Christians are called to warn people about sin and judgment out of love and concern for others. It's not about them but it's about others. Although they are tasked to do some soulwinning but the issue they have with sin is about others. For Christians to warn the person of their sins is out of love. They know the consequences of sin are deadly and they don't want the person to perish in their ungodliness. They don't want people to go to Hell but to Heaven because they know a holy and righteous God has to judge sin and the unforgiven sinner someday. But the problem is that people tend to always shout, "Don't judge me!" It's a sad fact that so many people on Judgment Day are going to be told, "My servants tried to warn you but what did you do? Didn't you say don't judge me to them? Now I'll judge you because you died in your sins."
Christians are the most unloving people only according to worldly standards and the stupidity of political correctness. But in God's eyes Christians are the most loving people. If Christians didn't love people then they wouldn't have the heart to warn them about sin and judgment. They are called to love people so much that they hate the sin that's destroying people. If you must love the good then you must also hate the evil. God is holy and He must and will hate sin. Christians are God's adopted children through Jesus Christ and they too must and will hate sin. To be loving means to hate what harms others and to wish well for others. That's why Christians are called to be witnesses to the world.