I understand your comprehension of political ideologies is single-dimensional and tunneled, but please at least try to educate yourself.

You may start your reading here on socially left ideologies: https://en.wikipedia.org/wiki/Social_liberalism

And here's socially right ideologies: https://en.wikipedia.org/wiki/Social_conservatism

As far as politically left or right, that means in reference to the state's notion of left/right politics. In Israel, politically, alternative left is reserved for jihadists and other anti-Zionists, the left is reserved for the Zionist peace-optimistic camp, the right is reserved for the Zionist peace-pessimistic camp, and the alternative right is reserved for the pro-settlements camp.

As you may guess--or not, considering your comment leaves little hopes in that respect--this spectrum of left to right in no way corresponds to the ideologies professed by social liberalism or conservatism. A different order is required in order to redistribute those camps across a social liberalism/conservatism spectrum. And, indeed, split them up into new camps completely, as there are communists in the same camp as the jihadists, which are very much incompatible ideologies.

Many 'left-wing' politicians are socially conservatist and many 'right-wing' politicians are socially liberal.