There is a split between the Haredim and many National Religious on the issue of visiting the Temple Mount precisely because the Haredim ascribe no religious significance to the State of Israel. All begin with the assumption that it is problematic to visit the Temple Mount because it is so holy and there is a fear that (1) someone who is not careful with Jewish law may walk in a place that is forbidden for those who are ritually impure (from being in the proximity of a dead body) to enter, or (2) someone who has not immersed himself in a mivkeh may walk in a place which he may not enter. However, for the National Religious, there is a countervailing issue: if we do not show that we care about the Temple Mount, the world will think that it is not the holiest site of the Jewish people, and therefore in a peace treaty it may be handed over to the Palestinians. The Haredim don't care, as they do not ascribe any importance to Israeli sovereignty.
Palestinian reportedly shot dead by Israeli soldiers after approaching Gaza border fence (Haaretz)
from the article: Prominent rabbi to Peres: Jews forbidden on Temple Mount