I am not familiar with details of the chulent ban, but I think a very defining difference is that the “Hechsher Tzedek” does not involve itself in any Kashrus issues. Therefore what they are doing is coming up with an alternative definition of Kashrus (and a subjective one at that). In the chulent case it does not seem like there is any attempt to redefine kashrus, but rather the Eidah Chareidus (which is a community organization involved in numerous issue besides Kashrus) is refusing to do business with organizations that they feel are functioning in an inappropriate way. So if the “Hechsher Tzedek” crowd would be pushing legitimate hashgachos to boycott firms that do not meet their requirements in areas of “tzedek” that would be a similar type of idea, and the debate may be more about whether those requirements are legitimate. Instead they are attempting to push an entire separate “hechsher” that has nothing to do with Kashrus.
This is just my opinion of the top of my head, but it seems a clear distinction to me.