I have taken a look again at the sites that mention Portugal as the origin of Bejarano, instead of Bejar in Salamanca.
Some of these are more explicit:
"Su antigüedad se remonta a los tiempos del primer rey de Portugal Don Alfonso Enriquez, pues Fernando González Bejarano, Capitán general de dicho rey, después de haber conquistado a los moros el 29 de Noviembre de 1162, la ciudad Portuguesa de Bejar, tomó el nombre de esta por Apellido, llamándose Bejarano, apellido que se perpetuó en sus descendientes."
I don't know any place called Bejar in Portugal, but I do know that there is a place called Beja. It is possible that some of the Bejaranos do indeed descend from this Fernando Gonzalez Bejarano. However, all the Bejaranos with converso and Jewish ancestors will have descended from Bejaranos from Bejar, Spain, i.e. from Jews of the Aljama Bejarana. Fernando Gonzalez Bejarano won't have been Jewish but Christian, as he took part in a battle against the Moors. Therefore, he cannot possibly be the ancestor of all the numerous Jewish and Converso families Bejarano.
I think that it is safest to start from the idea that your particular family descends from the inhabitants of Bejar (Salamanca, Spain) rather than from the christian Portuguese Fernando Gonzalez Bejarano. Unless there are specific indications that your family descends from his.
I have a similar problem regarding the origins of Rivas/Ribas. Some families descend from noblemen who seem unrelated to the main Sephardic clan. For example the famous Duque de Rivas only has de Rivas as a title and is unrelated to the Rivas clan as such.
The general problem related to this might be that Heraldic sources are not always the most reliable source for the origins of the non-knighted families of a particular surname. I think that genealogical data are in that sense much more important than the limited and therefore misleading information we can get from Heraldic sources.