Is "curious if" improper to use compared to alternatives such as "curious as to" or "curious whether"?

"Curious if" is commonly seen and heard, but strictly it's not right. On the other hand I'd still prefer it to "curious as to whether". That infernal "as to" keeps popping up these days: "he asked as to whether", "they debated as to how", "she decided as to when". Just remove the "as to" from those, and others like it, and you'll see that it serves no purpose. It's just a bit of verbal Polyfilla.

So, to answer your question, "I'm curious whether" is the best solution.

Edit: On second thoughts, I don't think "curious if" is wrong. In theory it does create an ambiguity, but in practice it never would. But "curious whether" is still preferable.

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

This usage of "if" is equivalent to "whether" and is explicitly included in the dictionary:

if — whether

There are a few other examples of this usage:

I'm not sure if other people feel like I do.

Do you know if other people feel like I do?

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.