If you think marriage is the union of a man and woman, that's homophobic. Check.
If you think it mattered that your mother is a woman, then you obviously think that sex somehow matters to being a parent, and that might make you look askance at same-sex "parents". So, that's homophobic. Check.
The very use of "mum" and "dad" suggests that the sex of parents is important when it clearly is not. Therefore, the words themselves must be homophobic. Check.
If sex doesn't matter at all to be a parent, then when does it matter? It can only matter for surrogacy and seed donation and for one's own private adult desire, and if you think it matters beyond that, then you are not only a homophobe, you may be a pervert as well.
Gendered pronouns re-inforce the heterosexist mentality of sexual complementarity. So, gendered pronouns are homophobic as well. Check.
Marriage was the only institution that reflected the public importance of sexual difference. Now that this institution has been de-sexed, there is no institution designed to bring the sexes together. If it is no longer important to have an institution specifically set up to bring the sexes together, then it follows that it is no longer important to keep the sexes apart. Therefore, all sexual segregation (e.g. of public restrooms, locker rooms, dorm room assignments) must be homophobic. Check.
And sexually distinctive dress in public must be homophobic, too.
Feel free to add to this list.