When the Lubavitcher Rebbe encouraged his followers to lay Tefillin on non-observant Jews, the Satmar Rebbe spoke against it, saying not all Jews were worthy of the mitzvah (the same way most Jews shouldn’t make Aliyah in his opinion?). That was his wondrous Ahavas Yisrael…
Was RYT “disagreeing” for the sake of distancing people from the Lubavitcher Rebbe’s general bad influence (Brachos 63a)? No. Only Rabbi Shach was devious enough for that.
Did he hate the mitzvah of Tefillin? The “Meisis Rabbi” hated a great many mitzvos, but there’s no evidence for this one.
Maybe Rabbi Teitelbaum fell for Shaul Berlin‘s “Besamim Rosh” fraud. The Besamim Rosh (another Navi Sheker) says a Ba’al Keri should not wear Tefillin.