To respond to your question, under the 14th Amendment public accommodation argument being used by Colorado state government and the activists, the answer is yes.
The free speech counterargument is rooted in the First Amendment.
One has to wonder if the enforcement agency would be as dogged in its pursuit of “wrongdoing” if the complaint involved a request for a liberal bakery to produce a custom cake with an aggressively pro-conservative, pro-Christian theme; say a graphically antiabortion or anti-LGBTQ+ theme? Let the agency demonstrate its enthusiasm to enforcing the law equally. Otherwise, sue them.
Alternatively, the vendors could develop special pricing for offensive messages.
Want a pro-Trans coming out cake?
Sure. As an “offensive theme list” order, the cake’s price is $100,000.00 with a non refundable $25,000.00 deposit. And the cake’s creation will be outsourced to another bakery, minimum order time is six months, customer satisfaction is not guaranteed, etc. Discriminatory? Not at all. Anyone ordering from the offensive theme list will be charged exactly the same amount and subject to the same conditions.
More seriously, the misuse of state power alluded to in the article above is already here. There are a number of jurisdictions in the United States where deadnaming or misgendering or use of wrong pronouns has become an actionable offense under the law.
There are? I didn't know that! *shudders*