Can businesses refuse service for non-discriminatory reasons?

Nope. Businesses that are open to the general public can only refuse service for non-arbitrary reasons, and they are open to legal action if they are inconsistent. For example, you can refuse to let more than 50 people into your building at one time for reasons having to do with fire safety (even if the fire code allows more), and you can change the policy to a maximum of 45 or 55 based on your observations of customer behavior. But if you randomly decide on the maximum occupancy you will allow each day, those who get turned away when your number is arbitrarily low will have a case against you regardless of whether they are part of any protected class.

Thank you for your answer. Are there specific laws that use the language “non-abitrary reasons”?

“No shirt, no shoes, no service” is legal for refusal of service.

“Service animals only” for seeing eye dogs is also okay.

I suppose the difference there is that those are clearly delineated rules (i.e. a dress code, a rule about pets on the premises), whereas the situation I’m thinking of is completely arbitrary (i.e. you are refused service because the employee is having a bad day or doesn’t like your hair). I’ve been given conflicting information about whether or not refusals of this kind are legal (even if they are rare and mostly relegated to the hypothetical realm).

You cannot be arbitrary or capricious when refusing service.

@Demosthenes No, there are no specific laws that use that language. What you will find is phrases like “equal protection of the laws” and “full and equal enjoyment,” which US courts have consistently interpreted as requiring a rational basis for excluding people from places of public accommodation (an interpretation doubtlessly influenced by a parallel tradition in English common law, upon which US law is based). Viewed through this lens, acts of legislation such as California’s Unruh Civil Rights Act, the Civil Rights Act of 1964, and even the Fifteenth and Nineteenth Amendments to the Constitution of the United States could all be seen as not establishing protected classes (a notion that some people loathe) so much as declaring that exclusion based on certain characteristics is irrational/arbitrary in the eyes of the law (and thus prohibited).

Businesses in the UK can refuse service for whatever reason they like, on an individual basis, as long as it isn’t discriminatory. However, they generally avoid doing behaving this this as that would be an excellent way of going bust. One reason they might, is part of group action to boycott unpopular people, to try to force them out of town. Eg, someone who had been very popular and had recently died, left an empty house which was broken into and squatted. This squatting prevented the house from being sold on, which caused many problems for the family of the deceased and enraged the local community. The squatters could not be arrested due to a loophole which existed at that time. The squatters had no good reason to be there and refused to move on. When they found they were unable to buy food locally, they had to move.

Yes. We had a sign up in the shop that we had the right to refuse service to anybody. The only way we’d exercise it, though, is if a customer became belligerent and rude and insulting. Then we’d kick him out and never let them in again.
We had a guy sue us once, for ridiculous reasons. I had no idea it was brewing, and had been for 3 years. Rick knew, but didn’t do anything about it.
Then he sued us.
The fact that we had the sign posted was important to the judge who decided the case.

The management reserve the right to refuse admission. At least that is the way in works in ROI. Of course if the management is careless enough to say something like “I’m afraid I’ll have to ask you to leave your complexion is making the other customers feel uncomfortable”. Well then its time to find themselves a good legal representative.

In most western nations (or states in the cased of the US), a private business owner can eject you from their premises providing that they don’t make it know that it is for discriminatory purposes or if it is legitimately not for discriminatory purposes. They could have a group of customers who only come to their business to harass them, or vandalise the property. They should have a right to tell them to leave. The same if I was to have someone over to my place for coffee and the started throwing around my furniture. I would have the right to get them to leave.

Just for the record, signs that say “we reserve the right to _______” have absolutely no legal force, and a judge who thinks otherwise and uses the presence or absence of such a sign in their decision has committed reversible error. Fortunately for @Dutchess_III, nuisance suits are usually pretty easy to get dismissed. So assuming the guy’s reasons were genuinely ridiculous, the result would likely turn out the same if the case were to be tried again. But an appeals court would be well within the scope of its authority to order a retrial if the judge actually cited the sign in his official decision.