A common trope from the "right" of the Anglo-Catholic movement is that those Anglo-Catholics identified as "affirming" are not really Catholic at all, but merely latitudinarians who find inspiration in the devotional aesthetics of Anglo-Catholic ritual. This allegation is perhaps more common in the UK, where "Forward in Faith" and "Affirming Catholicism" are to a greater extent actual organizational entities, rather than the conceptual tendencies they denote in Canadian and American Anglicanism. (Most major Canadian cities have one and only one Anglo-Catholic parish, often resulting in a Margaret Street-style truce).
There are, I think, several problems with this analysis. It is clear that those Anglo-Catholics of a conservative persuasion regard new theologies of gender as an unjustifiable departure from Catholic Tradition. Moreover, they tend to be convinced of the "package deal" nature of Catholicism. However, while the Catholic Faith is certainly not an à la carte affair, it is difficult to see that "liberal" Anglo-Catholics are markedly less consistent in their approach than their "FiF" brethren, much less their Roman Catholic counterparts. (At first glance, it is vexing that Anglicans are vetted individually for catholicity while Roman Catholics are more or less given carte blance by virtue of their submission to Rome. However, the relationship between FiF and Rome is somewhat more nuanced. Despite recent enthusiasm for reunion, many who have gone before have been disappointed to find a church just as troubled as our own, and not a kitsch-free lace and incense paradise).
First, consider what "affirming" Catholics actually believe. The beliefs of these Anglicans about the Eucharist, and about the ministry and sacraments in general, is unrecognizable to Protestants, yet highly similar to that of Forward in Faith! In the Diocese of Toronto, where only one parish offers regular Evensong & Benediction, those who seek the Lord in his Eucharistic presence gather for devotion to express a common faith, whatever their disagreements on the qualifications for Eucharistic presidency. I may disagree with some Anglo-Catholics about whether a woman can be celebrate Mass, but my understanding of what happens when she does so comes straight from the Council of Trent.
Second, consider the nature of ritual aesthetics. Anglo-Catholics have always been clear that it points to a theological truth. Thus the idea of aesthetics being separable from theology is an artificial one to begin with. A "Forward in Faith" Anglo-Catholic may disagree with an "affirming" Anglo-Catholic priest's views on orders or marriage, but when he (or she) dons a chasuble, he is saying something about our faith in the Eucharist - something that our hypothetical FiF observer should find quite familiar - and not merely making a fashion statement. Even female priests, who obviously dissent from FiF's position that they are Teflon-coated for sacramental insulation, should not be assumed to have a Eucharistic theology that is indebted in any substantial way to the Reformation. (One English correspondent whose opposition to WO was not of the "impossibilist" variety complained to me that he had never heard a woman priest chant the Preface. Perhaps this is a pond difference, but my first Anglican parish - on the high end of MOTR by Canadian standards, but what most in the CoE would call "high" - had a female incumbent who unfailingly chanted the preface unless on the verge of laryngitis).
Third, consider the ecclesiology of Forward in Faith. If as is undoubtedly the case the Catholic Faith consists not only in aesthetics but also in the deeper truths they represent, surely one of those truths is that of the nature of the church. Yet in England, with the adoption of provincial episcopi vagantes, "traditional" (read, biological-determinist) Anglo-Catholic parishes, in order to preserve their gin-and-lace ghetto and Y-chromosomal understanding of the priesthood, have sacrificed almost entire the corpus of Catholic teaching on the episcopate. The "Bishop" of Fulham, for example, is not a bishop in any recognizable catholic sense, with no see and no presbyterium of his own. (A makeshift presbyterium is nonetheless often corralled, with faux Chrism Masses drawing crowds of Anglo-Catholics dissatisfied with the real one, and the PEV concelebrating with those under his pastoral care as if a diocese).
Despite our differences then on the question of who may receive the sacraments of vocation, we have broad areas of convergence, and both groups (or tendencies) have made concessions in order to carry on our life of prayer and faith as best we can under present circumstances. Forward in Faith, however, has sought friendly relations with groups such as Reform (most of whom likely to don't even know what a sacrament of vocation is, much less believe in their status as such), describing catholics and evangelicals as two sides of one "orthodox" coin. Thus, while AffCaths (who apart from women and gays are indistinguishable from FiF) are written off as "Protestants in fancy dress," actual Protestants are welcomed with open arms as comrades in the orthodox and apostolic faith!