Color me skeptical.
I'd like to see this assertion backed up. I seriously doubt it can be.
Show me a photo of it. Or if no photo remains, then at least name one single current resident of Fort Collins who remembers seeing these signs "often" in that area of Ft. Collins. Or a reference to any local newspaper article of the era that backs this up.
Personally, I suspect it's a recycling of the "No Dogs or Irish" meme.
And who knows where that one came from? Here's a plausible scenario I can well imagine:
Yes, there are plenty of "No Dogs or Mexicans" sign images on the web, but most are non-attributed as to their source, or are "reproductions" that the manufacturer brags "are made to look old".
For a couple dozen dollars you can buy a paper copy that's framed and which the seller "thinks" is an original.
There's a Jewish-discrimination-history museum collection that shows a sign supposedly from a Dallas Restaurant Assoc of the 1920's prohibiting Dogs and Mexicans, but the museum's notes about it show a blank space for the "Provenance" category - ie they have no idea where it came from. That doesn't prove it's a fake of course.
Elsewhere, I saw a discussion of a sign allegedly from the 1930s that some posters fervently believed was genuine, but another poster pointed out that it was in Helvetica font, which wasn't invented until 1957.
People who want to find racism under every rock and shrub generally respond to the above kinds of facts with, "Oh! So are you claiming racism doesn't exist and never existed?!"
To which I respond, "No, of course not. But when you wish to make your argument as strong as possible with large numbers of supporting facts and anecdotes, take care to not overstate your case by including unprovable, unattributed anecdotes that might be completely false, because while an over-statement has the short-term effect of boosting your argument with listeners who take at face value all of your assertions, long-term it can seriously weaken your entire argument when even one supporting piece of it turns out to be false, thus casting a pall of unbelievability over ALL of it."
Of course it was different in Nazi Germany. Some British landladies put out signs announcing "No Blacks or Irish" when the first West Indian immigrants were arriving in England. I wouldn't put it past some dive, some equivalent of a biker bar, of having a sign that expressed similar sentiments in some US backwater -- perhaps as a joke -- but I really doubt that places that wanted to attract a half-way decent clientele really put up signs like that.
"No Irish Need Apply" -- well it isn't a total myth exactly. You could find a few classified ads that said that in the 1850s in the US and Britain, but Boston politicians used to say that such advertisements and signs were common in the 1930s, an era when the Irish were the largest population group in the city. It didn't happen that way then, and even earlier such ads or signs weren't anywhere near as common as some people believe.