The correct option is A Everybody but the children can enter the cafe.
We use but as an alternative to except (for), apart from and bar to introduce the only thing or person that the main part of the sentence does not include. It is often used after words such as everyone, nobody, anything, anywhere, all, no, none, any, every.
But is used as a preposition when we put a noun or pronoun after it.
Option A is correct. It means that all can enter the cafe except for the children. The noun phrase 'the children can enter the cafe', which also acts as an object for the preposition 'but', follows it.
Option B is incorrect as the sentence construction is flawed.
Option C is incorrect as 'but' has been used as a conjunction.
Option D is irrelevant to the context.