R&R you are conflating Catholic social doctrine with institutional organization. You are either confused or deliberately obfuscating. Catholic social doctrine is civilizational reason advanced with Christ's intelligence and His call to go beyond. The Church institution is as you suggest "owned" by by the "right" as you suggest. For many yrs, if not centuries, the Church espoused, as you state, an "alt-right" world as well as church view. After partnering monarchical world view the church espoused "benevolent despotism" which has proved ridiculous and now it has - in "words" if not deeds moved to democratic view- for others but not them,
The "argument" you use is precisely why the Church - claiming its social doctrine as "Catholic"but acting otherwise is divisive and lacks credibility because it teaches one thing and practices another. 
Thank you for being a "model" for the problem rather than the solution.