I'd say off-hand that, except for maybe some teeth-gritting A-Cs, Anglicans wouldn't have a problem backing off from asserting that the Spirit proceeds from the Son. There might be a problem getting Anglicans to assert that the Spirit does not proceed from the Son in any way, which really seems to be the Eastern position as of now.
This isn't correct. In an "economic" sense (or often called "temporal" though this can be misleading) the Holy Spirit does "proceed" from the Son - the Latin Fathers sometimes spoke in this way, the Eastern Fathers typically with more precision, speaking of the procession from the Father (which is what the Nicene Creed was addressing; a "trancendent triadology", different from how the Holy Spirit is manifested by the Son) through
the Son, when they would speak of such a manifestation of the Holy Spirit via God the Word.
This differs, however, from the filioque doctrine that was taught by Augustine, and which became a
cause in the Papacy's schism from the Church of Christ.
Admittedly, the RC's have toned it down in recent times, even popularizing the phrase "proceeding from the Father and the Son as one principle", though this may just be an attempt at burying the controversy by way of a vague term (since one could say such is simply an "economic" affirmation, or all the while hold to an understanding condemned by the Orthodox Church on numerous occassions.)
At the end of the day, the phrase does not belong in the Symbol of Faith, for the following reasons:
i) it's an un-canonical interpolation, and on this basis alone is divisive (and worthy of condemnation - it's not simply divisive in the sense of "oh, why bother with something that'll upset those cranky Byzantines?")
ii) it's been the banner of a heretical
(different than what the Church has always believed, which includes here the right-believing Latins) triadology.
iii) even if softened and defended on the basis of solely expressing a "economic" or "temporal" triadology, is still bad news, since it destroys the parallelism of the genuine Symbol of Faith (relation of the Word with the Father/relation of the Holy Spirit with the Father), which was intended to discuss the "origin" of Persons in the Holy Trinity (or in the case of the Father, His being un-originate) in eternity. If an elaboration of the mission
and/or manifestation of the Holy Spirit is what is intended, then a separate statement on this (such as "proceeding from the Father, sent by the Son for our salvation" or perhaps "through the Son" as some Father spoke) would be in order, not something that just ruins this parallelism and can create confusion. Suffice it to say, something like this would require the consent of Christ's Church, and I seriously doubt it would happen (since it's unnecessary, and could itself be misunderstood - at least if it were to happen without an ajoining, clear condemnation of heretical filioquism).
btw., this subject is addressed very well (including the Patristic differntiation between the energetic/temporal manifestation of the Holy Spirit through God the Son, and the eternal/essential procession of the Holy Spirit from God the Father) in the book Teachings of the Orthodox Church
published by Dormition Skete