I have commented elsewhere on the confusions in the political landscape caused by blurring at the edges of the venerable political designations of right wing and left wing. Venerable because the terms were first associated with the seating arrangements in a long-defunct French parliament. See extract below (source, Wikipedia) .
The term comes originally from the legislative seating arrangement during the French Revolution, when republicans who opposed the Ancien Régime were commonly referred to as leftists because they sat on the left side of successive legislative assemblies.
To claim that a person or institution is today either left-wing or right-wing is to subscribe to a False Dichotomy: An advocate represents an issue as "black or white" when in fact the reality is "shades of grey".
The political false dichotomy left/right survives I suspect because the terms have become a shorthand description with which a protagonist can berate an opponent or claim group membership. "You are a leftie" is intended as an insult when used by a self-described RWDB (Right Wing Death Beast); "I am a leftie" is a badge of honour when used by a self-described leftie. And vice versa.
Neither label is very useful, given that the meaning of the political terms left and right in Western political culture have almost inverted on several dimensions over time (eg authoritarianism).