I doubt that Tedd's father would be so accepting of it right off the bat. I mean, this comic should be plenty of evidence to that. If he really did know and understand what gender fluid is, he would have put two and two together by now, just like most of Tedd's other friends did. At best, he's going to need some time to understand and get used to the change, and that isn't an easy change to come to terms with.
But either way, we can at least agree that Tedd's dad has to know at some point; Tedd can't keep avoiding it forever.