Political Weirdos

When two persons/groups choose to use the same label, it becomes harder for anyone external to differentiate them easily.

Calling the people that confuse the two as "irrational" and bigoted isn't going to clarify anything, and will likely cause them to assume you are not allied with them.

Dismissing people who have concerns that those confusions might be used by bad actors is just gross naivete.

But, certainly, restricting the political power (or human rights) of a particular based on their chosen labels--even if those labels are confusing--when they espouse tolerant views and act in tolerant ways IS bigoted.

The closest analog I can some up with is "Catholic". If you just use that label, I think I am justified in assuming you do not value bodily autonomy (particular of women), and are therefore not a tolerant member of society. I'd certainly welcome a "Catholic" that makes it clear they reject intolerant Catholic dogma, but the existence of tolerant "Catholic"s does make it easier for intolerant Catholics to acquire and use political power. Of course, "Muslim" and "Islam" don't come with quite as formal an organization or consistent a dogma, so it's even more confusing.