This mother has labeled her own child "transgender"
before that child has the brain capacity or adult sexual experiences to label him/her self.
Questioning the mentality of this mother is not homophobic.
Some background might be helpful. I am in my late 60's. In grammar school, I was attacked on my way home from school by a gang of eight classmates, led by a mentally disturbed boy my age who perceived me as a sissy. They encircled me, tore my clothes, punched and kicked me. I got my punches and kicks in too. They retreated eventually, and I was never bothered again. I take some grim satisfaction that the gang leader later died young of alcoholism. Life wounds all heels.
I live with a man who is also in his late 60's. In 1990, while eating ice cream with his male lover in Boston's South End on a hot summer evening, he and his lover were attacked by an adolescent gang of several Black-Latino residents from a nearby city housing project. They were both nearly stabbed to death with dozens of wounds, as well as being punched and kicked unconscious. Their neighbors, out on stoops in the heat, simply watched. None would give a statement to the police. And the police asked the victims when they came out of coma what they had done to provoke the attack. The Boston Police failed to find even one suspect for this horrendous attack.
These are two cases of anti-homosexual violence which could be related correctly to the fear-hatred which is called "homophobia". One of the markers of true "homophobia" is its general social acceptability, even among those who know homosexuals they like or even love. It is irrational. Imagine if the these same stories above had been placed in a context of anti-Semitism when they happened.
Today's LGBTQ+ mob (from whom I dissociate myself as a gay man) have taken the word "homophobia" as a weapon against anyone who expresses any opinion, no matter how scientific or considered, which diverges from their goose-step political line. I believe the political elite of that mob foster this kind of fascistic blind loyalty and enforcement of their ideology to keep themselves in six-digit Washington jobs. Every elite needs an enemy against whom to mobilize its followers against threats to its validity. American-European corporate capitalists need "The Russians", for example.
Since "homophobia" refers to a senseless fear-hatred of homosexuality, a sizable segment of the LGBTQ+ mob cannot experience "homophobia" when getting negative responses to their behaviors or appearance. Why is that? Most transgender activists demand that their condition not be associated with homosexuality. They strongly differentiate between sexuality and gender. So, how can they be subject to "homophobia"? And, logically, how can they be considered part of a gay (homosexual) rights movement? "Transphobia", another term of dubious merit today, should be better defined by those who throw it about. It should not be considered relevant to a gay (homosexual) rights cause.
I do not maintain that senseless fear-hatred of homosexuals has evaporated. To the contrary, I feel that hatred of homosexuals has rebounded, largely due to their association with ideologies which are either irrelevant to homosexuality or directly a threat to homosexuals, like religious ideologies. A blind complacency in the gay and lesbian population has allowed this to happen by enabling through unquestioning financial support organizations like Human Rights Campaign and local Pride non-profits who have surrendered to religious, transgender, queer/questioning(?) and bisexual subgroups within. The bullied have now become bullies in LGBTQ+ contexts. They have hijacked the gay rights movement.
What's not homophobia? It is not homophobic to resent a mob which tries to silence an intelligent and articulate opinion about anything. It is not homophobic to resist mind and speech control of any kind. It is not homophobic to question the sanity or medical ethics of castrations and mastectomies, performed on disturbed adolescents with or without the permission of their parents. It is not homophobic to react negatively to a screaming mob of people who dress and act like rejects from a circus audition while demanding to be taken seriously. It is not homophobic to defend homosexuals in the face of murderous religious ideologies, such as fundamentalist Islam, Judaism or Christianity. For example, it is not homophobic to protest the defense of Islam by misguided LGBTQ+ activists. It is not homophobic to suggest that you are not a homosexual unless you naturally desire and prefer to have sexual intercourse with a person of your same gender.