There are different indications in teshuvos from rav Moshe – he clearly forbade CS to be served in yeshivos, to teach children to be careful when there is even a chashash issur. On the other hand, he calls it a chumra and not a din elsewhere.
MTJ talmidim have always told me that rav dovid was meikil mainly because he held there’s no inyan even for a baal nefesh. Rav Reuven holds that there is and he only started being makpid on CY a few years ago.