Are all controversial matters subjective or relative?

Question

Yes.

con·tro·ver·sial (kŏn'trə-vûr'shəl, -sē-əl)
adj.
Of, producing, or marked by controversy: a controversial movie; a controversial stand on human rights.
Fond of controversy; disputatious.

Disputatious means the subject can be argued -- which means there is more than one set of beliefs or opinions. That's subjective.
subjective

adjective

Based on individual judgment or discretion: arbitrary, discretionary, judgmental, personal. See opinion, surprise/expect.