Greene is not claiming that trans people do not exist.
Except for the fact that she is claiming that there are only two genders, so that is exactly what she is doing - she is saying if you are male by sex, you MUST BE male by gender, i.e. of you are male by sex, you CANNOT be female by gender, therefore you are wrong, therefore your kind don't exist.
She is pointing out that they are not the gender they may demand to be considered.
Except for the fact that this is untrue.
Again, it bears repeating - sex and gender are not the same thing. The science of psychology is very clear on this. Feeling that your sex and your gender do not match is a real thing, it actually happens to people, and it is NOT, repeat NOT a choice they get to make.
That is not denial of rights or privileges.
Except for the fact that for people to be treated as equals and not be discriminated against for characteristics they have no choice over, is a fundamental right. Black people don't choose to be black, gay people don't choose to be gay and transgender people don't choose to be transgender.
Advocating against that, which is what Greene has done, is advocating for a denial of rights.
She has proposed no penalties for believing oneself to be a gender other than what they are, nor has she proposed any for pretending to be a gender that one is not.
Discrimination
is a penalty. Opposing legislation to grant rights to people who suffer discrimination
is in effect, allowing a penalty to continue to be imposed.
What she has chosen to highlight is that it is a violation of other peoples' rights and privileges to deny them the freedom to view reality independent of the "feelings" of someone else. A woman is an adult, human, female. A man does not become a woman by "feeling" like one. They become "a man who feels like a woman" a "trans-woman"
What a load of supercilious, ill-informed horse cock.
Transgender people, and their existence has ZERO EFFECT on people who are not transgender. It does not effect their rights or privileges; it does not change anything about how they go about their daily lives. But the discrimination YOU are advocating for (and lets be blunt, you are at the very lease a supporter of the homophobic, anti-LGBTQ crowd or you wouldn't be arguing on Greene's side of the debate) has a very real, very damaging psychological and emotional impact on people with gender identity issues.
This was Green's clear intent with her sign, to cause emotional hurt and distress to Newman and her daughter.