I have not really run into this much. I do go back to what some consider 'mythological" but I am not so sure. Many times science (archaeology, forensics, dna, etc) has proven mythological people or places. I take some with a grain of salt and do not add them to my line, and some I do, such as Harald Fairhair as even the Norwegians and Swedes accept him as real.
I go directly back to Herman Isaac Op den Graef who is a well-known Linen Weaver and Mennonite Bishop from Kreigsheim, Germany. His parentage is in much dispute as some claim he 'has no parents', meaning they are just unknown, and there is a huge amount of people who believe he is the child of a morganic marriage between Julich of Kleves and Anna Aldeklerk and related to most of the royal houses of Europe. This one I take with a huge grain of salt and I do not add this extra line to my trees. I believe it could be a possibility, but until proven, it is not something I am willing to add as I want my real ancestors and lines.
With all this said, we need to be very careful we do not take down possible lines that are questionable with some probability. I have read very credible discourses on how and why King Arthur is real as are the characters in Beuwolf. None of were alive during this time and so we truly do not know.
It used to be believed that the Coelacanth fish was extinct and an ancient fish whose fossils had been found and these fish lived millions of years ago. Then a fisherman brought one up in 1938 which spun the heads of scientists and Darwinists of the day. This fish was not supposed to be alive, and yet the Japanese had been fishing for them for centuries. Prior to 1938 people would have told you you were crazy had you said you believed these fish were still alive- but they were. I feel the same way about many of the legendary people whom we are told were not real, though there is reason to believe they were.
If a person seems way too bizarre, or if the information does not have enough substantiation, disregard it, which is what I do.