Yekke2, if you’re around, I’d appreciate your input here.
Not sure what input you looking for!
The debate regarding wearing tefillin on Chol Hamoed dates back to the Rishonim, of course. Tosfos in Menachos 36b writes that one must wear tefillin on Chol Hamoed, wheras Tosfos in Eruvin 96a writes that Chol HoMoed is an Ois. As far as Nistar is concerned – הנסתרות לה’ אלקינו; I can’t help you with that. In the world of Nigleh, the discussion is whether Chol HaMoed is considered an Ois (two primary discussions: a) Does the Issur Melachah of Chol HaMoed constitute an Ois, and b) Does the Issur Chometz/Chiyuv Sukka constitute an Ois).
As far as Halachah is concerned, the Tur brings both opinions, and the Mechaber and Rema argue about it in O”ch 31. Wearing Tefillin on Chol Hamoed is not Ba’al Tosif even according to the Shittas that חול המועד לאו זמן תפילין, because you are doing it מחמת ספק, and your כוונה is only on the tzad chiyuv. (Not that simple as far as the Rishonim are concerned, but bottom line Halachah it isn’t a problem. See Magen Avraham 31.2)
I don’t know whether it would be considered a chumra or a kulla. The consequences of wearing tefillin in the wrong time is זלזול יום טוב and זלזול תפילין, and the consequences of not wearing tefillin is possibly being מבטל an עשה, although not necessarily. (See here for further discussion.)
Reb Moshe does not allow wearing Tefillin in a shul which does not, or vice versa (Igros Moshe O”CH Chelek 4 Siman 34), both because of לא תתגודדו and מפני המחלוקת. As far as Eretz Yisroel is concerned, see Igros Moshe O”CH Chelek 4 Siman 105.4.
[Geordie613 – See R’ Moshe Shternbuch here.]