People's Party is left-wing? from what i read its a right-populist party critical of immigration.
Their welfare policies are very leftist and eradicating poverty is their core goal, but they have at times criticized that taking in too many refugees could harm welfare for the disabled and elderly.
The Reykjavík Grapevine writes that a well-known xenophobe has recently joined them.
https://grapevine.is/mag/articles/2017/09/22/dawn-of-the-populistsProfessor in political science Eirikur Bergman recently called them "a radical Socialist party" and he is the author of "Nordic Nationalism and Right-Wing Populist Politics: Imperial Relationships and National Sentiments" so I suppose he would know if they were right wing populists.