The reason they're focused on defending Islam's compatibility with American values is not that they prefer Islam to Christianity, it's that they're trying to counteract people who claim that Christianity deserves a privileged position in the Anglo-American public sphere. They're trying to push the needle away from the "Judeo-Christian ethics" understanding of Americanism, not place it all the way over at sharia.
A major problem I have with political argumentation like this (and I am not attributing the argumentation to you; I recognize you are describing an observation) is that there is rarely if ever a limiting principle given.
I don't really care about the distinction between "They are trying to set the needle at sharia" vs "they are trying to push the needle in the direction of sharia (for completely unrelated-to-sharia reason)". If there is no limiting principle on the pushing in that direction, then I have every reason to believe that the end result of this pushing is sharia, regardless of what the pushers want.
Explaining explicitly where you want the needle to stop is one limiting principle. The only other limiting principle I have ever seen elaborated on, which only came after an hour of arguing, was "people like you (ie. me) who vote against what people like me (ie. the guy) want". That's a fine limiting principle! However, if that's the terms of the discussion, then that's an argument for me to adopt the most extremist right-wing position I can, since after all, I don't want extreme right-wing-ism, but I want to move the needle in that direction, and the more extremely they're pushing in one direction (sharia is pretty extreme, to keep the example up), the more extremely I have to push in the other direction to counterbalance.
That limiting principle seems legit, to me, from a philosophical basis, but I don't think it's a particularly good idea. On the one hand, I really do not want large groups of people pushing literal naziism any more than I want them pushing literal sharia, even if it's just a tactical gambit. And, on the other hand, "you can't push for literal naziism, that's evil" is routinely deployed as an argument (AND FOR GOOD REASON), but if we've already implicitly agreed that nobody holds these positions for their own sake, but just as tactical needle-moving strategies, then 'naziism is immoral' is no longer a good argument against tactical naziism