Question: does Halakha allow Jews to enter homes/businesses of idolaters who have open shrines?

Hi, for context, I am a Buddhist. A while ago I asked on this sub if Halakha allows Jews to enter Buddhist temples because I was curious, and a lot of people seemed to agree that it does not (though there was not full consensus). Today I had the thought: lots of Buddhists and Hindus who don’t have enough room in their homes to have their shrines in a designated shrine room just put their shrine in a room that is also used for other things – I have done this in the past when I didn’t have room (in a place that I could cover if needed), and one of my friends also has his shrine in a common area of his home (on the floor because he is Vietnamese and they often have shrines at floor level, so he can’t cover it). My grandparents have their shrine open as well, on a shelf in a common part of their home.

Also, many restaurants run by Asian people, both East and South Asian, have open shrines. I grew up in and right now live in California and have seen this often, and I’ve also lived in various places in North America and also some places in Asia and have seen this. Actually, in South Asia it’s common to have religious iconography in various rooms of the house even if you do have a shrine room! For example, I lived in Nepal for some time, and the (Buddhist) family from whom I sublet a room had a shrine room upstairs, but had a smaller shrine in the kitchen/dining room which was also actively in use (for giving offerings and such).

So then, must Jews eschew entering such common rooms and businesses if they want to keep Halakha? Since the room is used as the place of worship? Or is it fine because it’s just a section of that room, and the main purpose of the room is something else (such as being a living room, or kitchen, or restaurant, etc.)?

Thanks for anyone who can sate my curiosity and blessings to everyone.