A forbidden word.
In the antiquated sense, a realist is someone who believes reality (in the antiquated sense) is coherent, governed by mathematical laws.
There are three kinds of realist, the classical, the modern and the post-modern.
The classical realist is someone who believes reality was created by an all-powerful, all-knowing, all-wise God, who invented the laws of reality, including the laws of nature.
The modern realist is an agnostic, who believes that nature is governed by mathematical laws, but has no idea how they got there.
The post-modern realist is an atheist who believes that natures laws are purely random. In order to reach that conclusion, the post-modern realist hypothesizes an infinity of universes, all governed by laws that come out of a dice cup, or something else more crude than a warehouse full of monkeys set to type out at random until, someday, Shakespeare's plays emerge. We just happen to exist in a universe whose laws actually make sense and whose laws give rise to intelligent life which is capable of contemplating such laws. How all these universes came to be, however, relies on quantum theory, which is a mathematical theory of nature. If this all sounds a bit like the story of the great serpent that survives by eating its tail, welcome to the club.