BRTD, I think the thing that really offends Jews is the trade name "infringement" as it were. If the Messianic Jews called themselves something other than Jews, or Jews for Jesus, it would be less of an issue. But it is a free country, and Jews don't have the exclusive legal right to the name, so that is that. It is complicated by the term Jews referring to both a religion and an ethnicity/tribe in common parlance.
I always like to think about how Christians would react if a Muslim evangelical organization started a group called Christians 4 Mohammad that claimed they were authentically Christian, but accepted Mohammad as the final prophet and adhered to the five pillars of Islam.
If an Islamic group (hard to analogize this in America to someone like Santorum) started doing joint appearances with Christians 4 Mohammad and said this showed their outreach to the Christian community, and I don't see why all those Christians just don't get over themselves and be broad-minded and accept that they're Christians too blah blah, well we can see how successful that would be.
There's also a very long and ugly history of Jews being compelled to convert which animates the Jewish reponse.