Vannakkam: Firstly, I meant no nonHindu, not no Hindu. Restrictions to groups within religion has been going on for a long time. Non Catholics can't receive communion, non Brahmins aren't allowed in moolasthanams, nonMormons, and Mormons not living up to standards cannot enter their temples. The list goes on. In countries it's similar, and simple things like barring people with criminal records get people turned around from the border gates.
The reasons are similar ... keep the inside pure, others out. Hindu temples are by law, private places. If a devotee comes drunk or disorderly, the temple authorities have every right, just as private citizen has, to boot them out. If a temple board has decided to ban people with mustaches, so be it. There are many temples in South India where men must remove shirts. When in Rome, do as the Romans do. Obey the laws of the country you're in, whether you agree with them or not. If not, it can get you in a ton of trouble.
So why are non-Hindus even wanting to go into a Hindu temple? Mostly it's curiousity, but it could also be other reasons, like terrorism, desecration, etc. Besides that, the definition of who is a Hindu varies a ton. Although I may not agree with a really stict enforcement, UI respect the right for a temple to put it there, and there are several good reasons for asking non-Hindus to stay away. Deciding who is or ho isn't is a very tricky matter.