Adjectives and nouns referring to the ideas, actions, documents and members of specific political parties, movements and groups are capitalized. ... a Liberal policy paper (of the Liberal government or party) New Democrats. a Progressive Conservative government (refers to the Progressive Conservative Party)

Should Socialist be capitalized?

Communism, capitalism, socialism, and solidarity need caps in headings and articles? Your three "isms" are common nouns and should not be capitalized (except of course when they're the first word of a sentence/title/heading/etc).

Should Marxist be capitalized?

Unless they are derived from proper nouns, do not capitalize words for political and economic philosophies. Examples: democracy, capitalist, communism, Marxist.