If cilia flush mucus from the nose and antihistamines stop cilia function, wouldn't prescribing the antihistamine be counterproductive?

Good question: Even if antihistamines may have an effect on muco-ciliary clearance from the nose, the drug does not completely eradicate mucus clearance and the benefit of the antihistamine should out-way any effect on ciliary movement. Viral infections have a more profound effect on ciliary motility. I doubt that antihistamines "stop" ciliary function. The drug is only indicated with allergy.