No, it has to do with "Gack!, you want to cut off WHAT!!?!?!

"
Find some way of having it come into fashion with the Roman ladies, so to speak. And for the health benefits to be more obvious. Put those two together and suddenly it doesn't seem so unlikely. If you need another reason, make it so that the legions adopt it as a sort of "test of manliness" type of thing.
Also, you could have Judaism play up the monolatrist aspect; basically, tolerating the existence of other religions while still thinking that they're wrong, or at least not as correct. That would allow for a more gentle and gradual adoption of it by the Romans.
The food restrictions are the trickiest thing to get around. What you might end up seeing is some sort of dispensation by which you only have to follow the dietary restrictions if you can afford to sacrifice things like pork and shellfish that would normally have been in your diet. As a result, being able to strictly follow all of the laws becomes a sign of wealth and prestige.