I don't think I've come across homophobic people who would willingly use the phrase "embraced his homosexuality". That IMO acknowledges that homosexuality is something a person cannot change.
Homophobia is pretty specific, it's fear and/or contempt for homosexual people. That tweet does not seem to suggest that the author is fearful or contemptuous of the father. It's actually just using the father as a means to attack the son. It's not even using the fact that the father is gay to attack the son, it's using the fact that the father hid his homosexuality (or denied it, or whatever) to attack the son, so I don't think it comes across as anti-gay (which is subtly different to homophobia).
Sure, it's a rather insensitive thing to say, but nothing more.
Homophobia is pretty specific, it's fear and/or contempt for homosexual people. That tweet does not seem to suggest that the author is fearful or contemptuous of the father. It's actually just using the father as a means to attack the son. It's not even using the fact that the father is gay to attack the son, it's using the fact that the father hid his homosexuality (or denied it, or whatever) to attack the son, so I don't think it comes across as anti-gay (which is subtly different to homophobia).
Sure, it's a rather insensitive thing to say, but nothing more.