kosher food rules helped reduce sickness

There's been a lot of pushback against this lately. For a long time (a very long time, going all the way back to antiquity) there was a strong academic tendency to try to "rationalize" traditions and taboos and provide practical explanations for their purpose, and current scholarship has taken a second look at that and found the evidence wanting in most cases.

This is an active area of debate right now so I don't think there are any solid answers, but what does appear to be fairly well agreed upon is that Kosher rules did not meaningfully provide for a more sanitary lifestyle than would have been found in the surrounding non-Jewish communities in most cases. Everyone got sick, including Jews, most of the time. The ancient Jews who developed the laws were surrounded by pork eating, beef-in-milk cooking peoples, and despite an inordinate amount of historical scrutiny there's no evidence for differing health outcomes.

As for the Black Death specifically, some Jewish areas may have been somewhat spared plague for reasons that probably had nothing to do with their religious practices and everything to do with their status as outsiders with less direct contact with the broader community. Plague spreads via flea bites and inhaled aerosols - handwashing before meals really wouldn't any difference.

But also... they weren't really spared at all in the big picture, Jewish communities were also hit very hard by the plague in many places (and some Christian communities inexplicably spared in others - it was just uneven), and the idea that they were somehow untouched and that's why they were killed is just the echoes of medieval anti-semitism. Research actually suggests the European Jewish community suffered more than the Christian community, because they were disproportionately city dwellers and cities were disproportionately affected.