Litvishe Chareidim are called “Yeshivish”,as well asl those with Chassidishe backgrounds who grew up in Litvishe Yeshivos.
Litvishe Charedim can be and probably are in Bikur Cholim.
I’m not sure the point was that only Chareidim work in these organizations. Rather I think the point of the OP was to combat the negative impact that a few crazy Chareidim have had in the media by pointing out that Charedim are responsible for some of the largest chessed organizations.