Hating relatively harmless sins shows that love the sinner and hate the sin is hating the sinner but denying it
 
The core Christian doctrine is that God loves the sinner and hates the sin.  Because he loves the sinner he detests the sin for that is an infestation of evil in the person.  We are to have the same outlook.  The doctrine is an evil distraction from the fact that we automatically hate any person we fear.  Fear causes hate. You cannot divorce hate for sin from hate for the sinner.  Indirect hate for the sin is still hating the sinner.  Indirect is a good smokescreen.  You cannot use that trick to hide your hate.

Loving the sinner and hate the sin enables you to get at a person for harmless sins. Think of how the Catholic Church seeks to convince a teenager who enjoys a little masturbation that he or he is doing something heinous and worthy of expulsion from God forever! The Church gets away with it thanks to the doctrine of love the sinner and hate the sin. It is a good smokescreen. It lends a degree of subtlety to the Church's injustice and evil. The Church should be severely punished for abusing that teenager with its lies and hypocrisy. The love the sinner and hate the sin is about looking good as one destroys the dignity and rights of another.
 
Many sins are relatively harmless. For example, sex using a condom. Incorporating blasphemy in comedy is another example. We have to remember that people often take offence at things and this is their own responsibility. If you are offended it will not kill you.
 
If you hate harmful sins and people believe that you are still able to love sinners, then they cannot say you hate harmless sins and love the sinners. If they say it they will not be saying it with a straight face. Nobody believes a person who claims to love sinners when he says that harmless sins deserve punishment. Nobody believes a person who goes as far as Jesus Christ to claim that they deserve everlasting torment in Hell.
 
If you claim the right to condemn even harmless acts such as masturbation or kissing an idol god as grave sins then you are consenting whether you realise it or not to others condemning you as a sinner for putting honey on your porridge or for using blue toilet roll or whatever. You demean yourself and ask to be demeaned by this right you claim.
 
Christianity says we do little else but sin so even if it were possible to love the sinner and hate the sin one would need to be a hero to achieve it. No wonder when we seldom if ever love God above all things. And Jesus commanded that all love is ultimately to be given to God which is even more impossible.
 
The principle of love sinner, hate sin makes a sinner of the person who washes a cup for a user or ingrate. That is doing a favour for a person who is taking good but won’t be loyal to good. But since Christian scripture tells us that we are all sinners and if you have unrepented sin all your actions are sinful because you have an attachment to sin and don’t really mean to be really good, it follows that practically everything we do is a fault. God has a problem with it and it is a sin.