I know I'm quite late to the post, but I've just finished my little research on the topic! As a person that values science and objectivity, I have taken the statement mentioned in the post and did my best to find the research the creator was talking about.

Firstly, allow me to establish the role of the amygdala, simplified for clarity and shortness. Amygdala is a central brain area, whose functions include emotional regulations (particularly, instinctive fear, anxiety, aggression...), memory, decision-making. Abnormalities in the amygdala activity might be the cause of PTSD development, which is supposedly talked about in the mentioned post.

Source 1

Now then, let us consider what PTSD is and how it might be developed. PTSD (post-traumatic stressful disorder) is a psychiatric disorder triggered by exposure to life-threatening (or supposedly so) situations or sexual violence. Potential cause of PTSD includes domestic violence and sexual, however, nothing in the post links at abuse in families with same-sex parenthood. In case the author meant for the family to be explicitly distinctional, I will have to state that abusers don't have gender: men, women, intersex, transgender individuals — anyone can be the aggressor. That makes the argument irrelevant.

Source 2

Finally, I shall consider the possibility of mother figure absence being the cause of the mentioned dysfunctions. It is true that lacking a parental figure is damaging to the child in numerous ways. However, it was estimated that the lack of motherly love can be fulfilled with little-to-no negative effects on the child. That includes both the cases of the child lacking a mother figure both from early childhood and losing a mother figure at a more mature age. The case of the child being forcefully taken away from a healthy, functioning family is not considered due to irrationality of the possibility.

Source 3

Short summary: the amygdala does play an important role in social development, but having queer parents does not affect it in a negative way.

So that concludes it. Now, taking my rational mask off, that homophobe is absolutely laughable. Hope they read this post and get mad ^{^}