I agree, but I want to add something from my perspective on this. I don't think nurturing, emotional sensitivity, or introspection are feminine by fiat; such that they are "feminine traits." I think if a masculine person is nurturing, and the act of being nurturing is part of that masculine person's gender expression, then nurturing is
masculine for them; not that we have a masculine person with a feminine trait.
I think that a lot of the problems that come from toxic masculinity is the perception that feminists want to "feminize" men, and that traits should be associated with gender. So the toxic masculinist, in an attempt to conform to their toxic idea of what masculinity is, actively avoids traits they perceive as feminine no matter how virtuous those traits are, and they pursue toxic traits they perceive as masculine no matter how toxic those traits are*. This problem I think ultimately comes from considering traits gendered by fiat at all.
(* -- Edit: On a re-read, this part sounded like I was associating masculine traits with being toxic. To be super clear, I'm only saying that the toxic masculinist tries to adopt all perceived masculine traits,
including the toxic ones.
Not that all masculine traits have varying degrees of toxicity.)
When I say "gendered by fiat," I mean something like across the board: that nurturing (for example) is always feminine, no matter who exhibits the behavior.
I think these traits are only gendered when a) the person exhibiting the trait likes gender and b) considers the trait part of their gender expression. So a masculine man that is nurturing and considers nurturing part of his masculinity is an example of masculine nurturing. A feminine woman that is nurturing and considers nurturing part of her femininity is an example of feminine nurturing. And a person, regardless of gender, that exhibits nurturing but doesn't consider it part of their gender expression is just nurturing; the nurturing in that case is not a gender-expressive trait.
Hopefully any of that wall made any sense. I still like your post, and feel like I'm splitting hairs.
Edit: also thanks to
@9-10ths_Penguin for his post that armed me with better verbiage to express this than I was trying to use.