Those days, many invaders of Islam and Christians stolen all the valueables in Hindu temples.
Further, Non-Hindus never bothered to respect Hindu deities. Normally Hindus will not enter any temple without bathing or with dirty clothes. Further, they do not do anything inside the temple, which is not accepted by the society.
The above mentioned were the reasons for not allowing Non-Hindus in some of the temples. But since the society has developed a lot and there will not be any more invaders (we have lost almost everything) and nothing leftout now...These temeples which do not allow non-hindus should change their attitude. They can allow non-Hindus by taking an oath from them that they will respect our Hindu deities. Further, they can also ask the non-hindus to have a bath before entering the temples.