Quagmire's Dad is not transphobic

At least not intentionally. It's true the episode makes fun of sex surgery and made Dan Quagmire a bit stereotypical (although it's not nearly as bad as Mrs. Garrison in South Park). However, pretty much every character in Family Guy is a stereotype in some way. What people took most offense with is most of the characters' transphobic attitutes and Brian's reaction to sleeping with someone transgender.

I can see why the reaction with Brian at the end is in poor taste, and half of the crowd will laugh at it and half won't. However, I can still see the main message of the episode. The attitudes presented are not shown as being okay, and Quagmire matures as well. At first he's very critical and even angry about his dad making the surgery. Near the end though, he learns to accept his (now mom's) new identity and loves her for who she is. And that in itself is quite a thoughtful message. I think the problem lied just in how the episode was structured, but at heart it's clear it was made with good intentions.