The original post is a learned discussion, as is the correct answer alluded to by Reb Eliezer, but the rest of the responses are largely born of ignorance.
Chassidim in general (including Chabad) wear R”T tefillin for the latter part of Shacharis or afterwards. What Chabad does differently is that the Rebbe a”h instituted that bochurim should also wear them (contrary to implications in the Tur and Shulchan Aruch that only those steeped and habituated in Chassidus should wear them, which traditionally are not descriptors applied to bochurim). Sefardim also wear them, but they do as the Beis Yosef states to wear them simultaneously. Litvishe generally don’t wear them, as per the Gr”a, and the implications regarding being steeped in Chassidus.
The answer alluded to by Reb Eliezer is rather simple. It is known that the machlokes as to the Seder HaParshios preceded Rashi and R”T by many generations, so we want to be yotze both orders. But we don’t pasken like the R”T regarding the ink, so we aren’t choshesh for it.