SSPX priests and religious, and I suppose Third Order members, owe Bishop Fellay obedience as long as they continue to be connected with the Society.
In the SSPX Third Order Rule, there is nothing about obedience to the SG of the SSPX.
I've heard otherwise, from a Third Order member. He is an accordista, as far as I can tell, and said so during a discussion on obedience.
I would be curious where he got that. Because my copy of the Rule says nothing about that. In the letter I received when I joined, it says:
Remember your commitment to the Rule:
A/ Daily obligations:
1/ Morning and evening prayers
2/ Recitation of the Rosary
3/ Attendance at daily Mass, if possible, or a quarter of an hour of prayer. (Not the Novus Ordo Mass)
B/ Confession every two weeks, if possible, or at least once a month.
C/ A retreat at least every two years.
D/ Recommended reading.
E/ Fasting on Ember Days, Vigils, and on Fridays
F/ No television!
In the Third Order booklet, it reiterates those rules, in slightly modified format. I see nothing in the Rule part of the booklet (or anywhere for that matter) about obedience to the SG. Frankly, it's hard for me to picture Archbishop Lefebvre writing in the Rule, "G/ Obedience to the Superior General of the SSPX." That seems bizarre, and if I'd read such a rule before joining, I would have asked what it meant, and probably would not have joined. I am trying to imagine how that would play out in the real world - for a layperson to promise obedience to the SG of a religious order. Suppose my wife joined, and a conflict arose between an order from the SG and me, whom would she be obliged to obey? In any case, the Rule of the Third Order is not binding under pain of sin anyway.
If you can find out from your accordista friend the chapter and verse from the actual Rule of the Third Order where it says that, I would be very interested. Perhaps they’ve changed the Rule in recent years to
add that? If so, hate to break it to +BF, but I do not feel bound by a Rule I never signed up for.
It does say, under Professional and Social Duties:
"2. To promote and defend the social reign of Our Lord Jesus Christ in society,
to combat Liberalism and Modernism, scourges of modern times which are delivering the Church to her enemies."
So as a faithful Third Order member, I feel bound to combat Liberalism and Modernism, even if they come from the SG of the SSPX.