the child of a Jewess and a gentile

Tosphot holds in at least three places in Shas that the child of a Jewess and a gentile is not Jewish. [for example Kidushin 75 Tosphot first words ור''י סבר לה כר''ע וכו נינהו. 
Also יבמות ט''ו ע''ב תוס' ד''ה  אמוראי 
This is obviously not like the Rambam.

This is obviously relevant nowadays to groups that pride themselves on being Jewish when in fact it can be shown historically they are descended from mixtures like this. If people's sense of pride and identity was rather their effort to learn and keep the holy Torah --that would a lot better. This whole idea of Jewish pride seems vacant to me. 

Sephardim have a private approach to Ashkenazim. They say Ashkenazim are not Jewish, but they feel they have to pretend. But they definitely feel they are not the same tribe nor kosher.[Any Ashkenazim in  Sephardi community will experience an enormous amount of pressure to leave. There will always be at least one Sephardi determined to get rid of the Ashkenazim at all cost.] Still in all history books about the original conquest of Islam, the general rule was Muslims took Jewish wives as spoils of war. Therefore Spanish Jewry when exiled to North Africa always made a point to write ס''ט  ספרדי טהור in cases when they could trace their lineage father from father back to people that were certainly Jewish. That is why ס''ט is how the Rambam signed his name and Bava Sali also.
Outside of a few amazing people like Bava Sali the general problem in the Sefardi world stems from their origins from Muslims. This seems to create a kind of problem that still exists. If they would simply be committed to keeping Torah then I would have nothing to say, but instead their commitment in Israel seems to be to find fault in Ashkenazic Jew and then to try to kick them out. 
As one fellow mentioned to me they have the trait of Sedom and Amora [That fellow I believe is from the family of Bava Sali--at least I know his wife is a granddaughter of Bava Sali's older brother David. The one that was martyred.]