Devils advocate: Having the required indicator on a field with values present shows the user that they should not attempt to clear that value. 

Then make it yellow instead. Something a little less attention commanding to the eye.

Here’s a good example of where it would be beneficial to the UX.

OK.  I’ll admit that looks pretty ugly. 

I believe you can override the border color of required fields if you want to make them yellow.   But I also am sure you will want empty fields to be red… 

The option to choose an alternate or no colour would be great.