If these are the only "doctrines" you are going by to determine which "house of worship" is right, then you will have to concede Islam is right - they don't allow abortion, homosexual marriage and certainly not women preachers. You're going to have to use a bit finer criteria if your claim holds any weight.
What I have experienced is the more closely a denomination holds to the Biblical truth of the Gospel of the grace of God through faith in Jesus Christ the more conservative they are in "social" issues and the more consistent and unified their congregation is.
It is actually because they are born again by that evident word of Truth of the Scriptures, whether they even saw the Bible it came from or not, that they are thus more prone to follow it after (unless they place man higher), versus preaching a message that depends upon hearing it from an approved church or dependent upon it.
In the latter case, converts may be moral and conservative if their church requires it, as well follow as its doctrinal errors, but the majority will also follow its trajectory as the church goes more South, as seen with Rome.
But if they follow the more sure, stedfast, firm, word of prophecy Peter points them to, Scripture, (2 Pt. 1:19-21) then they should never be moved.
Meanwhile, it is indeed a paradox that the section of Scripture that RCs resort to (Ja, 2:16-26) in seeking to provide a positive contrast btwn their church and that of sola fide types indicts their church as being liberal overall and her members as inferior to the evangelicals they attack.
Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works. (James 2:18)
“What I have experienced is the more closely a denomination holds to the Biblical truth of the Gospel of the grace of God through faith in Jesus Christ the more conservative they are in “social” issues and the more consistent and unified their congregation is”
You just described the Catholic Church for the last 2,000 years. Thanks for the complement.