I agree that it's not incorrect, but "often we go to the museum," sounds a little unnaturally in my opinion. Maybe it needs a comma if used as an opening clause. "Often, we go to the museum." Even then, it sounds like an incomplete thought, like a reason or circumstance must follow why or when we go to the museum. It's just how it sounds to me personally
I'd say that the Polish speaker has in mind a specific museum, or there is only one in town that is worth going to. They would phrase it differently if they wanted to say that they frequent all of them, like "Lubimy chodzić do muzeum" - "We like/enjoy going to a museum". But you have a good point.
My understanding of this sentence doesn't imply one museum but museums in general. I think I'd compare it to going to the theater or the cinema, which at least in Polish don't suggest going to the same one over and over...
By the way, I started typing "do you often go to..." in the search bar and the first two results were "the cinema" and "the theater", so do those imply going every time to the same... building?
The usual meaning of "are going" is that it is happening right now. But often refers to something that is repeated multiple times. These two ideas conflict with each other. There would be very limited situations where you sentence would be correct but they're probably too obscure to be counted as correct here.