That's because some people conflate Jewishness with Liberalism. Of course this is not true, as attested by the significant Jewish and philo-Semitic presence on this forum. But the problem with Levy et al. is that they themselves are often the ones doing the conflating, thus causing endless confusion in the population at large, as well as providing grist for the mills of neo-Nazi anti-Semitism.
"Christian" Leftists do the same thing. In its most extreme form, I'm thinking specifically of the so-called Liberation Theology types in South America.
But your solution is the correct one. Simply having these people change religious affiliations would be like changing the dust-cover on a book; the contents remain the same. They need a complete spiritual overhaul, to exorcise the (Satanic) influence of Liberalism and replace it with Orthodoxy.