There is that rumor but no current tested proof.
Two years ago, my allergist said to stop taking Benadryl (as a sleep aid) because of the study showing a link to dementia (due to it being anticholinergic). OTOH, a month ago my ENT said that the basis for that association is “very loose” and that consistent lack of sleep is much more likely to contribute to dementia than Benadryl.
There is all kinds of correlational evidence for several classes of anticholinergics — dismiss it if you will with the “not causation” quip, but I will no longer take first-generation antihistamines or other drugs such as antidepressants with anticholinergic characteristics. Take a later antihistamine instead such as cetirizine — a physically larger molecule that doesn’t usually pass the blood-brain barrier — and see if it works for the long-covid mitigation.