Kinda. But it gets fucking crazy. Mr Garrison gets surgery to be trans fem. Kyle gets taller, black skin, and Mr Garrison's testicles as his new knees. Gerald becomes a dolphin. It's all over the place.
Matt and Trey use the writing technique of "but, therefore" which leads to very insane story threads (with their ribald thinking)
Southpark makes fun of literally every and anything, so yeah it could be considered transphobic lol. Just keep in mind the intention is to be gross, over the top, nonsensical, etc...
Eh, life is short, might as well find humor in things, if we tip toed around everything anyone could possibly get offended for, the world would be a pretty bleak place.
South Park is always "edgy" in the safest way. Climate change was widely ridiculed when they made manbearpig, and the undertones of this one were definitely pretty bad. I give them a pass on mr/Mrs garrison because he's always been a piece of shit much like cartman, but the message with Gerald and Kyle is "surgery doesn't change who you really are." It dropped in 2005 so... Product of the time I guess?