Like you say people’s individual views could be either.
Here for example is an interesting take from the Huffington Post on the issue of abortion ( about which I have no desire to start a debate) and political leanings. The author identifies herself as being a “ lefty” ( her words):-
Abortion is one of those rare political issues on which left and right seem to have swapped ideologies: right-wingers talk of equality, human rights and "defending the innocent", while left-wingers fetishise "choice", selfishness and unbridled individualism.