this follows the established lines of "us versus them". When the mother discovered her son was gay she expanded her concept of "us" to include gay people- and suddenly she's a crusader for people who are just like her family. Had she discovered the homosexuality of anyone else in the world I believe she (and more importantly, most people with the "us versus them") mentality would happily condemn their different life situation.

tl;dr: she didn't grow, she accommodated.

Edit: I wrote this while I was still waking up at 5am and I realized this morning that I passed judgment against this lady. It is unfair for me to speculate about her state of mind, and as other commenters pointed out, her words did show signs of actual growth. Sometimes people take lots of small steps toward being accepting, and I acknowledge that this was likely a step for this parent.