Basically a Restaurant becomes public when people are free to enter and leave . That it is in a private place , funds provided
by self are all not concerned to the visitors. So restriction on the basis of caste , religion. If it is done, it offends Article 15.
Of course the restaurant will be a public place. You cannot open a public place and restrict the entry on the basis of caste or religion. Article 15(2)(a) of the Constitution says that the owner of a public place cannot discriminate and restrict or refuse the service on the basis of religion, race, caste, sex, place of birth or any of them.