The "Is valid Xhtml" validator for Rich Text Field in Sitecore does not accept Html valid attributes like: role, aria, data-... etc.
Trying to find a solution over the internet led to the majority of answers which were to disable the validator, which makes an area for the content author's error. Also, there were suggestions to make the change directly in the Sitecore file, which also has one drawback - makes upgrades a bit more difficult in the future.
This link has shed some light on the final solution: Override XHTML validation for Rich Text Fields in Sitecore

After some investigation, it was found, that under the hood "Is valid Xhtml" validator is utilizing XSD schema for the validation process. Happily, there is a way to extend it.
Here are the steps:
It includes the original xsd file (via "xs:include") and extending necessary element (via "xs:redefine") with additional for my case attributes.
Place it in MSVS project in the next hierarchy of folders "sitecore\shell\Schemas\[Customer Name] Sitecore xhtml5.xsd". Make sure file's "Build Action" is "Content" (right click -> properties):
And there are no more errors regarding undefined attributes.