Recently posted to academia.edu, an essay by Annette Yoshiko Reed entitled “Parting Ways over Blood and Water? Beyond ‘Judaism’ and ‘Christianity’ in the Roman Near East”, another piece along the lines of “the ways that never parted.”
I will not, here and now in any event, expatiate on the fundamental thesis, but note that there is some consideration of the Didascalia within this essay, in particular the issue regarding ritual washing. The essay rams home the manner in which the rabbis and the Didascalist redactors inhabit parallel (and possibly overlapping) intellectual worlds within the same physical space. In particular I note the comment in Tos Ketuboth 7.6 expanding a comment in M Ketuboth 7.6 regarding wives who are put away without their ketubah. Already the Mishnah notes a woman who speaks with a man in the street (cf. DA 1.8.26) and to the Mishnaic categories the Tosefta adds “who washes and bathes in the public baths with just anyone” (cf. DA 1.9).
Beyond quotidian bathing, and turning to the more central (for one redactor of DA at least) issue of ritual bathing, Reed states: “Although typically read in terms of a Christian rejection of Jewish ritualism or legalism, the concern for repeated washing is also paralleled among some Rabbis of their time”, citing Tos Yadayim 2.20. I cannot see how such a conclusion is derived from this text, but note it nonetheless as indicating a debate within Jewish circles, even as DA indicates a similar debate within its own Christian grouping.