Word for having strong political opinions but no consistent "side"

Solution 1:

I'm not sure there is one word or phrase for such a person, although in some contexts the term independent covers a lot of idiosyncratic political views. And there is a class of people who call themselves "economically conservative but socially progressive/liberal", however there is no one word for this (fairly common) type.

Solution 2:

Consider,

maverick.

a. a person of independent or unorthodox views

b. (as modifier): a maverick politician.

[C19: after Samuel A. Maverick (1803-70), Texas rancher, who did not brand his cattle] Collins English Dictionary

Maverick Dutch Politician Is Slain Before Elections LA Times

Leftist maverick Jean-Pierre Chevenement quit Tuesday as France's minister for law and order, depriving Socialist Prime Minister Lionel Jospin's 3-year-old government of one of the last remaining stars from its starting lineup. The mercurial interior minister, who twice before resigned ministerial portfolios and once rallied from a coma to return to public life, refused to endorse Jospin's plan for devolving a share of legislative powers to local officials on the Mediterranean island of Corsica. LA Times

mugwump

(Chiefly AmEng) A person who acts independently or remains neutral, especially in politics. [Massachusett mugguomp, mummugguomp, war leader.] American Heritage® Dictionary

Solution 3:

freethinker

a person who forms his or her own opinions about important subjects (such as religion and politics) instead of accepting what other people say

also

a person who forms opinions about religion, politics, morals, etc., independently of or counter to tradition, authority, or established belief

It's not a perfect fit since, although it can be applied to politics, it has a stronger association with religious thought.

Solution 4:

You can speak of a person having strong but eclectic (political) opinions.