Simcha: Cholov Yisroel is NOT a Chumra. Cholov Stam is a Kula. (Even the poskim that permit use of this Kula acknowledge that it is a Kula.) And not all poskim hold it is a valid Kula. In which case, to them, Cholov Stam is Cholov Akum and thus unkosher. If they hold it isn’t a valid Kula, they are prohibited from even facilitating or helping another Jew obtain Cholov Stam, even if the other fellow does use the Kula.
Your comparison to Beis Hillel/Beis Shammai is mistaken. A more apt comparison would be the MO Jew telling a Chareidi that you cannot eat the food from my home since my keilim were used to make Cholov Stam food and/or I used my pots and pans, dishes and utensils with food products using hechsheirim that you hold isn’t acceptable. Therefore I’ll feed you with prepackaged food with a heimishe hechsher and I’ll serve it to you on paper good and plastic utensils.
Beis Shammai certainly would not loan Beis Hillel keilim that Beis Shammai held is tamei since a) they wouldn’t keep such keilim and b) even if they had it, they hold it is tamei so they are prohibited to facilitate another Jew using it.