Harry's blood contains the love from Lily's sacrifice. Even though Voldemort is so full of hatred he can't possess Harry who's full of love, the small amount of love that went into Voldemort through Harry's blood was enough for Voldemort to touch Harry.
"Your mother died to save you. If there is one thing Voldemort cannot
understand, it is love. He didn't realize that love as powerful as
your mother's for you leaves its own mark. Not a scar, no visible
sign... to have been loved so deeply, even though the person who loved
us is gone, will give us some protection forever. It is in your very
skin. Quirrell, full of hatred, greed, and ambition, sharing his soul
with Voldemort, could not touch you for this reason. It was agony to
touch a person marked by something so good."
The fact that Voldemort can't touch Harry and the fact that he can't kill Harry are to different things: Voldemort can't touch Harry because he is full of hatred and Harry is full of love, and he can't kill Harry because of the sacrifice protection on Harry. Voldemort basically put a bit of love inside him so he'll be able to touch Harry.