A forebear (main accent on the first syllable) is simply an ancestor; there's no dispute there. To forbear (accent on the second syllable) means to abstain or avoid something; also no dispute. (Its past tense is forbore, and something could have been forborne.)
A problem occurs, though, with for(e)bearer. Sometimes a person giving a speech wants to find a more politically correct term for the now clichéd forefathers. They sometimes choose forebearers, which makes a certain sense because our forefathers had to bear the responsibility of government before us. But the bear in forebear stems from the verb be plus the suffix -er, that is, forebears are really fore-be-ers — they existed ("to be") before us. In contrast, the bear in forbear is from the word meaning "to carry."
Somewhere in the middle is the idea of to bear a child.
So with the e (forebearers), the extra -er is simply redundant — like engineerer (a person who engineers?) or pioneerer (a person who pioneers?). Without the e (forbearers), it ought to describe "a person who forbears," as in, "Those who chose to receive their cootie shots had no problems; the forbearers of the shots, however, were afflicted with the spontaneous amputation of their pinky toes."
So, by all rights, forbearers ought to always be defined as the latter. But you don't always have a dictionary handy, and neither word (forebear and forbear) is common enough that hoi polloi are tacitly versed in the differences. Using for(e)bearers to mean forbears happens often enough, though, that we might consider that a "new" meaning — one not originally intended — has arisen. (I write "new" because the usage would be new only to the dictionary; people have been making this "mistake" for a long time, so it isn't new in speech and writing. I write "mistake" because . . . oh, never mind.)
This is how language evolves. And, just like speciation, it isn't always clear when a new definition (species) has been created.
None of this is to be confused, of course, with Fourbears, a children's story sequel about interracial (err, make that interspecies) adoption in which Mama Bear and Papa Bear attempt to legally adopt Goldilocks, creating a controversy in the courts and ultimately leading an attention-starved Baby Bear into a meth addiction.