I dont think there’s any need to give the benefit of the doubt to these people anymore. You might argue they believe LGBTQ people shouldn’t exist, and I might believe you, but I tend to think their main motivation is just stirring up anger and resentment against the “other side”.
If people were concerned about privacy or safety, the us would have single user bathrooms or at least stalls that didn’t have 1in gaps around the doors (my 90s high school didn’t have stall doors at all, and in some bathrooms didn’t even have stalls, just a toilet next to the sink in the locker room). The same people aren’t upset about those things, because they don’t actually care about any of this.