this mutual opinion is coming from a conservative by the way

Why do you feel like a trans person who doesn't fit with either gender (non-binary is the term most use) would be invalid?

because you can't be non binary everyone has one of the two it's that simple

Why can’t you be non-binary?

because it's impossible to not look male or female or to not have any sex organs and other genderized features

Non-binary people can have either make or female sex organs
Sex doesn’t equal gender

if you have either or then you're female or male what's hard to understand about that and also sex and gender literally mean the same thing

Then how can a transgender person's gender be different from their assigned sex?

that's different non binary means no gender trans people have a gender

Agender means no gender, although it is a type of non-binary.
Non-binary people have a gender, it's just not one of the two that most are used to.

there is only 2 every category of people have 1 of the 2 no matter what they say

In this case, what if the categories are “one of the two genders society has normalized” and “not one of the aforementioned two”?