Let's try to cut through the weeds here.
Honestly, I'm not even sure where to start.
In short, she posted that anybody how identifies as anything other than "he/she" should seek services elsewhere.
I can say that Ms. Geiger's posts are probably ill-advised from a business standpoint. Even back to the days of Harvey Milk, businesses took financial hits for refusing to serve the gay community. If the bottom line is also her bottom line, especially in a state like Michigan, the more profitable thing to do would be to suck it up, use whatever pronouns a client told you to use, do what they want you to do, and take their money. With the statements that she made, and given the history of these stories, she's not just good lose business from the they/thems, or the zie/zirs, or ey/eirs -- she'll also lose business from a bunch of credulous people who are fellow travelers.
No free speech advocate can fix stupidity. People will vote with their dollars as they choose. I can't, and shouldn't control that. The government also shouldn't control that. You also shouldn't try to control that.
Ms.Geiger's original post was specifically about people who demand the use of neopronouns. I wish that she didn't eventually expand her comments to say that she's referring to the "TQ" portion.
This muddies the waters.
If you open your ears for a couple of minutes, you'll realize that there's a great many trans people who hate the neopronoun thing, and distance themselves from non-binary and gender queer people. If Marcus Dib, or Buck Angel, or Blaire White walked into this salon, there would be no pronoun problem. Even if Riley Dennis walked into this salon, as I doubt she would, there would be no pronoun problem.
The fact that Ms.Geiger later emphasized the Ts and the Qs means that she's buying into the bullshit, leftist ideology that trans is basically anything that differs from any traditional social projection. Ms. Geiger probably has some blind spots, and that's fine. If you come up to me and introduce yourself, and follow that up with, "I use they/them pronouns l." I'm not gonna work with you. It's not natural for anybody to say, "Amanda ran out to their car for a moment." It's dictatorial speech to command people to use language in reference to you, that they wouldn't otherwise use ("people" is plural, by the way, in case the reader doesn't know how language works). Still, most trans people don't play the pronoun game.
Most of them want to just live their lives in peace, and they'd be hurt to the bone if you asked them what their pronouns are; or, if they felt the need to offer their pronouns with every new person they meet.
I stand by the idea that Ms.Geiger has the right to sink or swim on the basis of her own ideas, and to the extent that she expresses them. Pragmatism isn't everything. I'll neither demand that people boycott her business nor shower it with clients on simple, political grounds.
The government shouldn't be involved in this. That's what I'll say. I'm sick of politicians trying to make names for themselves by attacking the opinions of many of their constituents for political gain. The only proper position for anybody with any political power is to defend free speech.
This is the time for politicians to actually be ambivalent, or flippant in their commentary.
"This is not our job. If people start harassing that salon, or the owner, or the employees, we'll get involved. You don't like what she had to say? Go cry somewhere. Not our problem."
There ya go. Problem fixed.
The government stays out, and everyone preserves the right to free speech and property as it stands.
If Ms. Geiger is producing a product so great that a zie/zim is willing to lie about the pronouns to get the hair done, it's a win/win. If Ms. Geiger isn't that good, the zie/zim can zim's money elsewhere.
The only way to lose is to get the government involved.