Without asking directly if one or the other; is there a way in a non-political conversation, to detect/sense if a person is democrat or republican in the U.S. or has tendency to be ?

-Or by asking what ?

The current tenets the parties might be a good proxy. If they support more than a couple of the MAGA favorites, they probably lean right, and if they like the so-called “woke” positions, they probably lean left. If they won’t shop at certain stores or use some products (owing to boycotts). How they feel about vaccines, education. Lots of topics have become political that aren’t inherently political.

13 hours ago, Externet said:

is there a way in a non-political conversation, to detect/sense if a person is democrat or republican

Since you're asking about Democrats/Republicans, I assume you mean Americans.
The easiest way is to ask what they think of D Trump; if they 'gush' about him, they are bat-shit crazy, and most likely Republicans.

In most other counties where the population isn't rabid about their politics, it is much harder to differentiate between Liberals and Conservatives. We care about the issues, not the party ( or their leader ).
I, for example, have voted Liberal and Conservative in Canada, and once even NDP ( Socialist ); I consider myself a social Liberal and a fiscal Conservative.

I think one thing that says they lean to the right is if they have a national flag in their front lawn. (This probably isn't limited to the US.)

"Have you listened to any good podcasts lately?"

As other noted, things that aren't inherently political. "Have you switched to bamboo toilet paper?"

The Right seems to have signed on to a lot of cultural posturing that's about not giving a shite. (or what you wipe it with)