It depends. I think it would turn sharply on a couple of things.
The underlying reason for the suit
Let us suppose that the business is a lumberyard that sells the customer roof trusses. The insurer has a problem with the trusses for complex engineering reasons: the store says the customer misapplied perfectly good product. Yes, that lumberyard can be expected to "86" that customer (at least, as regards to selling them engineered products LOL.)
However. If the suit is "you refused to sell trusses to me because I am Irish", that is a horse of a different color and should rapidly result in a ruling that "you can't refuse service for that reason". If the shop could simply change the reason to "you sued me", that would utterly defeat the ruling and civil-protection law generally - so yeah, that would be a "contempt of court" scenario.
Alternative sources for that thing
This was also trotted out in the Memories Pizza affair. "We're not the only pizzeria in town". (well there's ONE other in town; all others are at least a 25 minute drive).
The argument is the customer has a variety of alternative sources so they don't need this one. Versus the customer saying "No, I really don't".
But again, this turns on the facts and circumstances. If you're in a protected class, the business really can't turn you away on that basis. (imagine if businesses in the US rural south were able to turn away minorities on the basis of "you have many other choices. In reality, if every business does that, you'd have no choice and it would be a lie.)
I could also see this appearing in Right to Repair litigation. Manufacturers are often the only source for repair parts (e.g. because the are a vertical manufacturer or it contains propriety embedded software)... if a manufacturer litigated to stop a 3rd party repair shop from servicing their equipment, and lost, courts would take a dim view of the company then refusin to sell repair parts to the shop, since that would simply be another attempt to do what the court already said was impermissible.