There's no evidence of that. The problem was that Romans were occupying the country and installing their own Roman-friendly infrastructure, including Jewish priests.
Quite. Christianity manifested out of an incredibly idiosyncratic set of ideas that had been swirling around Late Second Temple Judaism in the 1st century BCE. The divergence of Christianity and Judaism took almost a century to really set in, and in large part that was through the conversion of impoverished or enslaved Greeks and Romans into Christianity, rather than Jews changing religions to escape Judaism.