Being a Muslim is to bow one's will to the Almighty. There is no such thing Wahabi/Hijji/Cultural Muslims. This is cleared in the Quran, that the religion chosen for us is Islam, not Islam Version A or Version B.
A Muslim will enter it knowing its importance, and though he may not be perfect in conduct, he would ought to ask for forgiveness.
Non-Muslims would naturally move about naturally, and end up doing things they do not know the gravity of, and over that not ask for forgiveness (from Allah). This is the reason in plain words.
For the Non-Muslims, my op stays as it is. Just because you are interested in sightseeing Mecca, doesn't mean we undo our own vows. Yes it is a beautiful place, you wanna watch it? Buy the tickets: "There is only one God, and there is no other God, that is the way straight". And you should be gladly allowed to sight see or pray.. whichever you want. Mecca's Hospitality would be yours.