I don’t knkw that it was “habituated suspicion”. I don’t think the Western European Jews believed that they had a dog in the fight between two interpretations of Christian theology.
In many cases I think it is anachronistic to judge contemporary movements by the values of their founders, although that is a factor to consider.
I was summarizing a thesis written by a Jew, Mark Nanos, in his book "The Mystery of Romans" (which is a very good analysis of Paul's writings from a Jewish perspective by the way).