Cisgender men being denied the right to enter female designated spaces is not "the exact same extent" of a denial as transgender women being denied the right to enter female designated spaces, for obvious reasons. The former group does not want to be accepted in female spaces as a matter of personal affirmation and does not claim that a lack of acceptance will negatively impact their mental health.

I get that you're playing devil's advocate here, and arguing the concepts rather than taking a personal position... but come on, buddy.
Those can only be asserted as being different if you develop ESP. From the perspective of an objective observer, there's no difference between male #1 wanting to use female spaces because they say they want affirmation and male #2 wanting to use female spaces because they say they want affirmation. The only way to tell the difference is to be able to read their minds and determine that male #1 is lying.
But before we even get there... why are the desires of the males in question being granted precedence in the first place? Why on earth should the desires of males - regardless of whether they're honest or not - be granted a higher priority in policy than the desires, safety, and dignity of females?
That's part of the problem with this entire topic! It centers the desires of males as the most important thing, and it relegates all female perspectives to a secondary or tertiary role.
Some males want to use female spaces, so the world (generally) steps back and starts considering whether or not the reasons that those males present are "good" reasons for them to get to use female spaces. People consider whether or not it would be "nice" to help those males feel better, and feel like the world accepts them the way *they* want to be accepted.
The fact that in doing so, females feel unaccepted, unaffirmed, and feel bad just doesn't seem to matter. The fact that this introduces a new level of risk to females, that it opens up giant gaping loopholes that would allow malicious males to exploit them and gain access to females when we are vulnerable... well, that's not a priority consideration. Because females just don't matter as much as males to the world in general.
When feminists talk about "the patriarchy", the surface level is males in positions of power and leadership, effectively excluding females from participation. The foundation, however, is that we live in a society that was developed by males, shaped around a male perspective as the norm, and that assumes a male point of view as the default for all decisions and policies. Even if it's not blatant, it's there. The male is accepted as the norm and the default, thus all aspects of society are
anchored in that view, and variance from it must be justified
to males.
From early childhood on, even when kids are allowed to play with whatever toys they want... juvenile males are conditioned to expect that they will get what they want. Males are conditioned to believe that their desires ought to be met. That doesn't mean they always actually get what they want, but it does mean that generally speaking, they expect to be provided with a good reason for why they can't have what they want. Males are conditioned to seek fulfillment for their desires, and to view their desires as a primary motivator. Males learn from a young age that pursuing their desires is a virtue.
Females are conditioned to subordinate our desires. We're conditioned to expect our desires to NOT be fulfilled. We're conditioned to hear "no" in response to our wants, and to not expect a justification for that "no". We are taught that our wants are not important - and that it's selfish of us to have wants in the first place. We learn from a very young age that suppressing our desires is a virtue, and that fulfilling the desires of other - especially males - is a laudable thing.
This is all a long winded way to circle back to "Why the **** should females be expected to have their mental health negatively impacted in order to positively impact the mental health of some males"?