Trans bathroom bans are ultimately just a means of driving trans people from public life entirely.
This is not an exaggeration, the anti-trans movement literally aims to "eradicate [trans people] from public life entirely", those are their words.
Here are some citations, numbers, and evidence to back up what you're saying and why we should view trans bathroom bans as genocidal rather than about safety, like anti-trans activists claim:
When laws permit transgender people to access sex-segregated spaces in accordance with their gender identities, crime rates do not increase. There is no association between trans-inclusive policies and more crime. As one of us wrote in a recent paper, this is likely because, just like cisgender folks, “transgender people use locker rooms and restrooms to change clothes and go to the bathroom,” not for sexual gratification or predatory reasons.
Conversely, when trans people are forced by law to use sex-segregated spaces that align with the sex assigned to them at birth instead of their gender identity, two important facts should be noted.
First, no studies show that violent crime rates against cisgender women and girls in such spaces decrease. In other words, cisgender women and girls are no safer than they would be in the absence of anti-trans laws. Certainly, the possibility exists that a cisgender man might pose as a woman to go into certain spaces under false pretenses. But that same possibility remains regardless of whether transgender people are lawfully permitted in those spaces.
Second, trans people are significantly more likely to be victimized in sex-segregated spaces than are cisgender people. For instance, while incarcerated in facilities designated for men, trans women are nine to 13 times as likely to be sexually assaulted as the men with whom they are boarded.
...
In society at large, between 84% and 90% of all crimes of sexual violence are perpetrated by someone the victim knows, not a stranger lurking in the shadows – or the showers or restroom stalls. But trans and nonbinary people feel very unsafe in bathrooms and locker rooms, though others experience relative safety there. In fact, the largest study of its kind found that upward of 75% of trans men and 64% of trans women reported that they routinely avoid public restrooms to minimize their chances of being harassed or assaulted.
These laws aren't designed to protect cis women, they are designed to police gender (this impacts cis people too!) and eliminate trans people.
Yes, the Catholic Church is anti-trans, but you have to understand that trans people are just like everyone else, they are subject to the same influences and pressures as cis people, and they come from the same backgrounds - from religious families, from conservative families, etc.
While trans people in the U.S. form an alliance with lesbian, gay, bisexual, asexual, two-spirit, and intersex individuals - this does not mean every trans person accepts the label "queer" or thinks of themselves that way, let alone how they think of other trans people. There are many self-hating trans people, and lots of trans people who hate other trans people.
Caitlyn Jenner is a Trump supporting Republican who went on Fox News to deliver anti-trans remarks about a trans athlete.
Blaire White is a Trump supporting Republican who makes a living supporting right-wing and anti-trans talking points on YouTube.
The Log Cabin Republicans are mostly LGBT+ folks who are Republicans, and they show up to support anti-trans legislation, like in the recent California vote to ban trans athletes.
I think you have to understand that labels like "queer" and "LGBTQ+" are political identities, and lots of people who are descriptively queer based on their sexuality or gender identity refuse to identify that way for political reasons. Some people remain closeted and hiding, but other people are open about their sexuality and just don't connect the dots between their sexuality and the political struggles of people with those sexualities, refusing to identify as gay or queer and instead just insisting they're "straight" even while openly engaging in queer sex.
Sure, it boggles my mind too, but it's unfortunately very common. I think a lot of this has to do with the dominance one identity has, like one's identity as a conservative or as Christian, over another, such as one's identity as a queer person. When those conflict, it's not surprising that sexuality or gender identity are not always the winner - especially in cases like Christianity where the religion can have a hold on your entire life (your job, your spouse, your whole family, your entire community - everything might depend on a religious identity like that and it's very difficult to escape). This is especially the case for a binary trans woman who transitioned so young and can live as a cis-passing woman, there might be very little visible about her trans identity at that point, making it easier to live as a conservative Catholic.