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I don't think you can classify the mother, with just what happen in this chapter, as homophobic. It was actually quite a normal reaction considering her age. She is a mother. And anyway, gays are still a minority and not as common to happen. Of course she wants her youngest and dearest son to have a child. That's something almost all loving parents wants for their children. That doesn't mean she is a homophobic tho. Homophobic requires a high level of hatred towards gays. Judging from how his mother reaction to the drama, according to the sister, she "doesn't care" as long as it's not concerning her family. If she's truly a homophobic she will go "what the heck, no that's disgusting!!" But she didn't. I suggest you to wait for the next chapter to see what will happen (i dont know either)
the mom is homophobic it's giving me the insatiable man war flashbacks. i want his father to show up and find out about him being gay and he's just nonchalant about it. like accepting and all