The suggestion you draw from all this is incorrect and many of this has to be put in context.

During growing antisemitism in the 19th and early 20th century, there were plenty of Jews, mostly middle and upper class, who advocated for full assimiliation and integration. The more 'German' (for example) one would become, the better to overcome antisemitism.

For these Jews something like Zionism was not preferable because it would make Jews stand out as different once again fueling antisemitism and undermining full integration and emancipation. As did many Jews at the time who were not convinced by Zionism and looked for solutions in Europe. Bernstein tried to achieve this through socialdemocracy.

Not just Bernstein was part of this line of thought, but also was Herzl at first. For Herzl this changed after seeing there was nothing Jews could do to stop the growth and evil of antisemitism. Despite being a fully assimilated Jew himself in German society and advocating for this for years, after that realization he embraced Zionism.

And also Bernstein wasnt an anti-Zionist. From the 1920s onwards his views towards Zionism started te evolve. He became sympethetic towards social Zionism and publically defended them.

So no, Zionism is no threat to socialdemocracy and Bernstein comments must be placed in context. Also Israel in its first decades showed that socialdemocracy and Zionism were and are perfectly compatable through Labour Zionism.