Can you love yourself while hating your sins?

No.
 
Religion says yes and some believers order you to do it in the name of God.  [You cannot love yourself if you agree with God hating your sins simply because love sin and hate sinner is impossible.  And if it were possible for us that does not mean it is possible for a God for God is too unlike us and unimaginable.]
 
So you judge your sin and not yourself! That makes no sense. To say you have sinned is to say you are a sinner - your sin is you. It is not the sin that can be condemned but the sinner. Judge your sin but not yourself is far worse than religion telling us not judge other people but to judge their sins.
 
Only a masochist will feel the required hatred for his own sins. When people suffer remorse it is because people were hurt and not because they broke a commandment. It's not the same as hating sins.
 
To tell yourself that you love yourself for you have some good qualities is really saying, "I am not worthy of any respect if I have no good qualities. I respect myself in spite of my sins." There's a deflating but there. It follows then that belief in sin blocks respect for yourself. The more things you consider sinful the more barriers you have to overcome to have respect for yourself.
 
Considering your good points is good but you must see your bad side as making you better and more interesting than a perfect person. This is the only way to succeed at becoming a better person and to do it without too much effort. Having to do things "in spite of" your faults is discouraging and flavours your efforts with negativity.

CS Lewis said we always have the generosity to love ourselves and hate our sins so we can do this for other people. If we really hate them we will punish ourselves with guilt. Hate is punishing yourself over some evil. If we do this wrong to ourselves over evil, then we are training and opening ourselves up to do wrong to others for the evil they have done or that we have perceived they have done. We are abusing ourselves and putting others under threat for we are training ourselves in evil. Hating sin makes it harder to forgive yourself.

Russell said that it is not sin that makes people unhappy but the sense of sin. Religion of course dismisses that as nonsense. Russell stated that envy ruins your happiness. Religion then says he admitted that sin makes you unhappy after all. It lies. Russell saw envy as wrong but not as a sin against God. Wrong and sin are not the same thing though they are often related. Wrong is just wrong. But sin is a violation against God's law. There is no need to regard wrong as sin and so a sense of sin does indeed make people unhappy and unnecessarily unhappy.

Self-love is the thing that has to be there for morality to be even possible.  Unless you love yourself you cannot consider morality important.  How can you be moral if you hate yourself so much that you think it is okay for people to hit and abuse you?  And that by implication insults other people too for you say they can be the same as you if they want to be.  Self love cannot be an obligation or commanded.  It cannot be a moral requirement for it has to be totally free and done because it is beautiful not because it is commanded.  You cannot command somebody to enjoy their coffee for that defeats the purpose. Thus the persons who love themselves is doing something far more important than morality.  Thus those who argue that morality in the form of God alone matters or is supreme in importance are doing you moral and psychological harm.

If you cannot love yourself while hating your sins there is no hope of you loving another while hating theirs.  Your hate turned inwards will only lead to you being a danger to them as well.