Objections have primarily focused on the sexual predator risk: that predators will use the Federal directive (or similar local laws) as "cover" to commit crimes in restrooms. But parents know their objections run deeper in ways they may not be able to articulate.
The American College of Pediatricians recently placed into words what most parents intuitively know: "Gender Ideology Harms Children." In a nutshell, policies that support "gender confusion" behavior in children inhibit the mental development process that normally leads to acceptance of one's own biological sex, and leads to a host of mental problems as adults, including a significantly greater risk of suicide.
Far from advancing "civil rights," those running the Federal government (most Democrats and a significant number of Republicans) are advancing a political agenda to further divide the nation against itself, to break down all institutions that could potentially challenge Federal authority: families, churches, bodies of religious beliefs, school systems, lower levels of government, and social groups and customs. Even persons who are self-sufficient can pose a threat (thus the need to "tax the rich").
This is only the latest of a multi-generational effort to condition the population to accept Federal control of all aspects of life without question . . . and without resistance.