He's Bipolar it makes sense one minute he hates clem the next he wants to help her
imo I don't think Luke ever hated Clem before. When He saw Clem's bite and dropped her he was probably scared and concerned that it was a walker bite. I wouldn't want to carry her knowing that she had a possible walker bite. What if she died in my arms and bit me as a walker? Even though Clem told them that it was a dog bite Luke couldn't possibly know that she was telling the truth. And later on when Clem wakes up after passing out, the group wanted to put her in the shed and he defended her and didn't want to put her in there. So I guess he was more scared of Clem turning into a walker or lurker as they call them and cautious then actually hating her.
This. He freaks out because he sees a bite, and he probably hasn't seen a dog in months, if not years. Secondly, it's not like he was about to cut her head off with his machete. Other than the time he dropped her, he didn't do anything bad to her.