They would need to preach something like that, yes.
In no way does that mean it is at the core of the religion.
The core of Christianity is Jesus, or at least I should think so.
Jesus said some nice stuff too about love and whatever, he also was a fan of slavery.
Now, to me, slavery doesn't come of as happy and love filled.
I can go quite in depth on that but I'll save you the reading expense.
Basically, my point is that plenty of religions have ulterior motives to their humanistic preaching.
Sure, though that's more common when they're hijacked by con artists and politicians. While there are religions that are started solely for the sake of such maneuvering, those seem more the exception rather than the rule, and rarely last very long before people catch on. Remember that for every con artist preaching humanism in the name of religion that you do hear about, there's probably a thousand genuine humanistic workers within that same religion that you'll never hear about because they'd make for boring headlines.
I'm not an expert, but the way I understand it, the "slavery" in Jesus's time wasn't necessarily the sort of thing we think of (though still quite bad by our standards). It's closer to servitude. Also consider that this idea of "any bad elements effectively negating, or rendering meaningless, any good elements" (or as you put it, "nice things") actually comes from a teaching of Jesus's. One that I find rather ridiculous, in fact. (That one about good trees being unable to bear bad fruit and vice-versa). Having a loving core doesn't necessarily mean that everything in the religion is going to be in line with that core, and in any case, we can't really be certain exactly what Jesus said in the first place.
But as far as I can tell, if Jesus had any "ulterior motives", they would have likely amounted to the ousting of Rome from that region. Whether that would have been a good or bad thing really depends on your overall opinion on Caesar and Imperial Rome in the first place.
I think it is unfair to call Judaism an ethnic religion. Maybe at first. These days they just take conversion seriously.
I didn't mean it as a negative, so I'm not sure if the stauts of "fair" is appropriate. It probably does depend a lot on which denomination it is, but if there's one thing I've recently come to terms with about Judaism, it's that I basically know nothing about Judaism.
It's been my impression that it's an ethnic religion, by which I mean conversion inherently means becoming part of a wider cultural identity and not just taking on a new set of beliefs and practices, but I could very much be wrong.