"What have you done for me lately?"
Those examples of Belkar helping happened a long time ago. He's already done enough bad for the team to completely prove himself worthless to the team or just too evil to be allowed in their group anymore. The second strip that shows Belkar being helpful is also not a very good example. He saved Elan and Durkon from death, but he wasn't really Belkar. That Owl's Wisdom somehow shifted his alignment to Chaotic Good and turned him into a halfling who cares about his friends and who actually enjoys healing the wounded. That is not Belkar at all. Also, he wants to see everybody dead, including the people of his village, for little reason or provocation. His only reason for not doing it is because he has enough sense to not put himself in a situation that ends with him dead. Unfortunately, he has no respect for Haley.
Let's see what Haley has against her.
- Shady class and alignment which seems to cause Belkar to have the assumption that the rules are more lax now.
- Lower AB and HP, so Belkar knows he doesnt have much to fear in regard to physical punishment as he did with the greatsword wielding fighter and Sneak Attack is harder to pull off in a one on one fight.
- She is essentially alone and Celia isn't much help since she is so non-violent. Belkar knows she needs him.
Haley was going to abandon him after he killed the oracle but they forgot that he did it in the first place, so she kept him around out of pity. After learning that he had been sick because he killed someone during their stay at the Oracle, she decided to let him stew.
If he hadn't killed the oracle they would have known how to get to Durkon, they wouldn't have ended up in Greysky and Belkar would still be able to fight outside of cities.
The reason for all the Belkar hate is simple, he's hate-worthy. He's vile scum. Even "evil" characters, or atleast the ones that hang with the good guys, either have a common goal and dont try so hard to derail everything or have good qualities or emotions for others that cause them to be more "human" but Belkar is almost devoid of it. The only people he's ever actually liked were Shojo and the cat.