I have heard that Jewish communities generally did not suffer as badly from the plagues because of religious washing and cleaning. Is there truth to this, and did this lead to Jews being blamed for causing the plague?
There is no solid historical evidence of the Jewish communities in Europe being any less affected by the plague due to the various religious practices regarding cleanliness, nor due to other practices in the Halacha (Jewish religious law) regarding behavior during plague times, which include some form of limited isolation of sick individuals.
This is because despite these practices (which were also not nearly universally enforced) other factors made these communities more vulnerable to the plague - Jews in Europe were mostly city-dwellers, and the cities were hit by the plague the hardest, and also because the Jews tended to live in tightly-knitted, dense communities, moreso than their Christian neighbors.
We don't know exactly how many Jews died from the plague, but circumstantial evidence suggests that the death toll was high. Many of the surviving documents from these times are eulogies and piski din (laws) regarding death and burial practices. On the other hand, few other developments in the Halacha were made during this time - no great interpreters, no important polmusim (a form of religious debate) were recorded - all of this suggests a community under siege by the plague.
Of course, the Jews suffered greatly from the baseless accusations of causing the plague, mostly by poisoning wells. Numerous pogroms happened during this time, with some of the worst occurring in Basel and Frankfurt.
For more on the subject, see: https://www.anumuseum.org.il/blog-items/700-years-before-coronavirus-jewish-life-during-the-black-death-plague/