I can't speak to how your first two sentences go as far as countering the point so I'll hold back. If that quells any fears is probably dependent on the person.
Is changing speech to be more inclusive anyone's right? I don't think anyone here advocated for any rights to be curtailed. People believe that it's a slippery slope situation i.e., where does it end. Why are we deconstructing people in to base bodily functions? Why is there a push for women to be called menstruators because a MTF might not feel included if we continue to connect women with periods? What is the purpose of such rash action to accommodate a mental aspect of a very, very small percentage of people?
I don't think people are worried about their children having more inclusive terms. For example, from the original post in this thread it is stated that some believe "this language is demeaning and reinforces harmful stereotypes" and that "replacing the term "vagina" with "bonus hole" is problematic as it diminishes the significance and complexity of female anatomy."
I don't think, I honest don't, that the pushback is all bigotry, man. I mean if you can admit that "bonus hole" is weird, why is aversion to the changing of speech in this way such a big leap? And this plays in to the larger, admittedly media-fueled, trans debate. Why should women accept biological men in to their spaces? Why should they be forced to compete against them in sports?
Sorry for all of the questions, I just don't get that side of the debate. To me, it seems like it has become less about these people living their lives the want they want to and more about us changing our worlds to fit their mental fantasy. I think I might've mentioned it before but I don't see the rationale to allowing someone's self-expression to determine their rights. It doesn't make a lick of sense. I'm black, a minority. I can't choose to be anything else. I can't fake white, I can't pass as white, I can't change my name to be more white and then demand everyone treat me as white.