Several people I know are nuts about this sort of stuff. I try not to bring up the subject.
The idea of "fulfilling prophecy" is nuts. The Temple Institute is nuts. The two Chief Rabbis of Israel would never agree to it.
I really don't think Israel would allow the demolishing of the Dome of the Rock or Al Aqsa Mosque.
The religious nuts consider modern Israel to be treif anyway ... among the first people to be oppressed, would be the majority of Israeli society, including the majority of Jews, who are rather secular. At least most Muslims and Christians there are religious, the majority of Jews are not.
BTW ... the fully Orthodox Naturei Karta Jews are opposed to modern Israel, including any Temple Institute stuff. Basically, only the Messiah can reestablish Israel, and the Socialist Atheist Jews who did, don't qualify.