You’re really making me work for it when you could just read it and back off:

The specific usage of “curious if” is perfectly acceptable in much the say way that “curious whether” is acceptable. It does not imply a conditional.

I’m curious whether other people feel like I do.

“Curious,” by the way, has a few other variants:

I’m curious if other people feel like I do.

I’m curious as to whether other people feel like I do.

I’m curious about whether people feel like I do.

To directly answer your question:

However, is it actually improper or logically incorrect?

No, it is not improper or logically incorrect. Which of these is more appropriate is a matter of personal and regional preferences.