Speaking personally, and not as a Cromwell descendant (although it is looking increasingly as though I am linked to a family where a rather impressive looking website confidently asserts the ability to trace the line back to the 4th century BC) I work on the basis that whatever anyone anywhere asserts, I am going to try to replicate their research and assess the source material for myself.
Having assessed the source material for myself, if I am persuaded by the evidence I mark it up. If I think the evidence is suggestive, but not determinative, then I mark it up as a "tentative".
I have no problem in following a tentative line as far as it goes, with whatever sources assessed for what they are worth.
If I traced a family line into an Anglo-Saxon or Norse royal line, then I might hesitate to include Woden in my tree (after all ... claiming blue blood is one thing; divinity is quite another
). However, the fact remains that the royal genealogies are there for all to see, and whilst plainly they become mythical at some point, they are nonetheless likely to be accurate for at least a couple of generations if not more.
Where you put the "tentative" marker up is, I guess, a matter of personal taste. But I certainly have no problem with including the "reputed" bloodlines, as long as it is clearly flagged that they ARE only reputed rather than confident attributions of ancestry; and the nature of the evidence on which they rest is clearly indicated.
At the end of the day, all genealogies are mere work-in-progress, and subject to change in light of further discoveries ...