My God is better than your God, and I’ll prove it by destroying your idols ?
See, it’s gone.
My God is better.
Many times the successor religion has folks who adhered to the old religion and they may well have thought of the old religious facilities as being as much a community meeting place as anything.
So they'll protect it with a bit of redecoration, and all is good.
Not everybody knocks down the old ~ in fact all over Europe there are Protestant churches that were formerly Catholic churches, and other than rearranging the altar about 500 years before the Catholics finally came around to the correct point of view on that weighty matter, you'll find nothing much at all has changed in the buildings.
Recent work at the kaaba in Mecca demonstrated that the original hindu temple aspect of the structure is still sufficiently visible to the trained archaeologists that they were able to prove that's what it was ~ but without the snakes.
Then, there's the church attendance records of the Moslems themselves. Pakistani islamic researchers have determined that for the first 300 years of Islam (and that covers the period when the building in question was built) Moslems attended Christian churches ~ and appear to have not made a big deal of it.
No doubt there's more work to do on that issue, but it's interesting that there's any evidence at all that they, themselves, in the early period, when they are supposed to be so wild and wooly, didn't consider it a big difference!.
Which raises the fifth issue in the debate, why did the sultan build the building ~ what was he thinking ~ not what do the paleos today think, but what did he think. Further, if there'd been a Jewish authority in Jerusalem at the time, what would they have done.
The point I"m making is that the ancients were probably not fighting our battles, but their own, and for the most part, there in the early stages of the Dark Ages, that'd be surviving!
But, if you want to tear it down, do it, but that ticket is yours ~ not the ancestors.