I personally haven't come across that issue yet. A good test would be to create a new test process with a blank form and just the components you are trying to test. Very important to start by testing with the basic default settings e.g. add the date field, make it required (don't change any other settings like format or calculations). Then hide it using the field rule as you've described (sounds like you're doing it right as far as I can tell) and then see if that works. If it does, make each additional tweak until you establish what it is that is causing the issue.

Also remember that you can nest sections (containing fields) within sections (containing sections, or fields). So that means you can have sections within sections that are hidden but configured to "save data" that may overrule individual field level logic. 

I can't reproduce it with a simple form only contains a radio button and date field. There is a known bug for hidden required field inside section when the section is hidden as well. If you can provide your download process and open support case, it will be easier for us to identify the root cause.