Yes, so it's all strange. I don't think Gil should touch Parker. The person you love is Lars, not me, even if you have touched me before.
When Walter was surprised that Gil had never touched Parker, Parker's answer was very unnatural. He summarized the reason as Gil's strong hormone secretion, which seemed like a lie. But from Gil episode, we can know that Gil used to be a pure person, which is a little contradictory.
Why did Parker interfere in the thing between "Lars × Gil" couple? Parker is just a friend. It's none of Parker's business. I think even the best friends should not intervene in the affairs of couple. This should be left to the couple to solve by themselves. I don't think Parker is a good man who has no brain to help others. Gil asked Parker to stop him while dating Lars, which was too strange. It seems too hasty to conclude that Parker is a good man and a good friend. It will appear that Parker is a flat character.