In general, in modern English, avoid capitals except for proper nouns. "Surrealist" and "surrealism" are not proper nouns.

Should art styles be capitalized?

Nouns and adjectives designating cultural movements, styles, and schools—artistic, architectural, musical, etc. —are capitalized if they derive from proper names: Aristotelian, Cartesian, Gregorian, Keynesian, Platonism, Pre-Raphaelites. ... The lowercase style is preferred to avoid an undesirable profusion of capitals.

Do you capitalize genres?

Don't capitalize genres (use opera, symphony, jazz-- not Opera, Symphony, Jazz). Remember this rule by thinking about genres in literature: you wouldn't capitalize Novel, Short Story, or Poem, either.