I would say "yes, and no". I agree that there is a correlation but correlations don't prove cause. I also agree that there are many churches with women pastors/elders who have not endorsed homosexuality (I know of a good number).
I think the correlation is best understood by the compounding variable of "basic approach to the Word of God", or "value of human wisdom in relation to God's Wisdom".
I would guess very few American churches come up with a complimentarian view by debating with their Bible's shut or left at home. Instead I think we can label such churches as for the most part "old-fashioned Bible thumpers". They hold (in general) to very literal interpretations of the Word of God and view human wisdom in general and there own wisdom specifically as vastly inferior to God's Wisdom.
A church that is not in the category I just described is going to be much more moved by cultural shifts. Clearly we are seeing one of the most rapid cultural shifts. I wonder even if Barak could have been elected for his first term with the pro-homosexual platform of his second term. As a nation we stand for few things so strongly as we do for homosexuality. Does anyone think our response would be so weak with ISIS if there were a group of homosexuals trapped by terrorist on a mountain facing death unless they decided to stop their sexual practices?
Anyway, without a strict and literal interpretation of the word of God and a view that God's wisdom is vastly superior to our own; we will be blown and tossed by every wind of teaching. I think that is the real correlation that empowers the correlation you are observing.
Is a church a "lean not on your own understanding church" or a church that believes that "some adjustments are ok based on what we think"?