Professor Legasov superstition in Chernobyl

In the next episode, the couple in the scene you're referring to...

turn out to be KGB agents. They're there to spy on Legasov. So her inquiry is most likely meant to see if he'll reveal the real reason for not wanting an upward-facing glass (that has likely been contaminated), or she's simply probing him with generic banter to see how he reacts and what all he says/reveals.

edit I'm unsure if this answer is correct or GlenRunciter's answer. I guess it hinges on how genuine the woman's reaction is, which I can't quite remember that accurately.

It's not a matter of the direction of a glass being a known superstition. It's a matter of Legasov's behavior being weird, and her assuming that he must engage in this behavior because of some superstition she doesn't know about.

Look at it from the point of view of the woman:

A man at the bar asks for a drink. The bartender makes the drink in a glass that is perfectly in order. The man stops the bartender, points at another, equally perfectly in order glass and asks to be served in that glass. Why would this man want to drink from one glass and not the other? There's nothing wrong with either of them.

To the woman who doesn't understand the contamination, there is no rational reason for Legasov to favor one glass over the other - the glasses are equally suitable to drink from.

Therefore, since there's no rational reason (in her mind), she assumes the reason must then be irrational, which is effectively what a superstition is.

There is one superstition involving the glasses: If the glass is kept bottom-down, the evil spirit might sneak in and then hurt the next person that will be drinking from this glass. The same could happen if you'd left your drink alone for too long - hence, the glasses should be kept bottom-up and drank quickly when full.

This superstition has actually roots in hygiene: if the glass rests for a longer period in a regular position, it might be full of various contaminations (especially in the dirty environment) - viruses and bacteria from the air (or in this case the radioactive dust). Also, in the pubs glasses that just has been washed are kept bottom-up to let them dry faster - this means that such glasses have indeed been cleaned, not just wiped by a dirty rag.

I really doubt that the KGB agent knew themselves about how serious the situation is - hence they just half-jokingly ask about Legasov's superstition. Judging by the bartender's reaction, he is accustomed to such requests.