It depends on how you use the term. Some people might call us “broad” (as opposed to “narrow”) complimentarians because we believe God’s design for sexuality applies to all of life (and not just to the precepts about marriage and the church).
However, for many of us, the term has become synonymous with the narrow variety. And with the pandering done by pastors and theologians who want to reduce male authority to a tie-breaking vote in marriage at best. To a weird fluke of God’s character (“somebody has to make the ultimate decision and for whatever reason God made it the husband”), a design bug that more or less came from the Fall.
We don’t believe sexuality is a design bug. We believe it’s a feature. We believe God made men and women differently. We believe it’s cool and beautiful. And we believe it has ramifications, one way or another, in every realm of life.
Here’s where it gets a little confusing. Many people who call themselves complimentarians believe these things too. But enough people have co-opted the term to mean “a non-ordained woman can do anything a man can do, and a husband should only exercise authority as a last resort necessary evil” … that many of us have decided to move away from the term.
What term do we use instead, you ask? Luckily nobody died and put me in charge of that committee. Personally I don’t mind the term “patriarchalist” since that’s really what I am. One who believes in father rule. But I dunno. If the patriarchalist bums some people out for whatever reason, I might be willing to meet them half-way, with some other term. If I’m in a circle where “broad complimentarian” tells people most of what they need to know, I’m happy to start there.