I’m not so sure.
First, I would say a program like Medicare for All is in fact a “socialist” program. It’s ‘publicly owned and operated’ medical insurance. But I wouldn’t consider a program like Social Security to be socialist since it’s really just a federal disbursement. This also doesn’t mean the economy itself is socialist; just that program.
Second, I’d say the socialist tag is important strategically. These ‘socialist’ program will materially improve people’s lives, and we ought to want people to know that they are in fact socialist. In my view, Fox News and all of right-wing media will call it socialist, and that’s what their base already believes. To them, Obamacare was bringing on full communism (obviously laughable). I think we ought to embrace that label and then flaunt it when people are better off when their medical and educational needs are taken care of. The Left has been scared of socialism for too long.
Just my thoughts.