The Answer is "Yes"

To this question:

One by one, the great institutions that gave meaning to Western civilization have fallen to their infection.  Our schools teach their false history, our universities enforce their fascist speech codes, our media coddle their thuggish political hacks, our military is seconded to serve their social rather than our national security agenda, courts are enjoined to consider “just outcomes” rather than due process,” and now even the elected president of the United States questions the logic of the First Amendment, the guarantee of free speech. 

Can they possibly have now also captured the Church of Rome?

First, they captured the Catholic Church decades ago, with enough force to bring about the Second Vatican Counsel.  The changes wrought to the Mass were enough to twist it away from what it should be, and towards what the Marxists want it to be - completely removed from the spirituality of the church.

Second, for decades the Church has happily handed over it's responsibilities to the governments whenever it could:  Feeding the poor, sheltering the homeless, helping the suffering.  It was just so much EASIER to let the government take over, don't you know, until Catholic charities are but a shadow of their former selves.  Still potent, still able to function to some degree, but still a shadow of their former selves.  This is a direct result of the Marxists inserting themselves into Church leadership and allowing their political ideologies to direct the Church's actions.

Third, they have allowed all the modern Marxist heresies to permeate the Church's branches to the point where a Catholic priest tweets out support of same-sex marriage, and when he gets fired for it, other Catholics react in shock.  Have they not even bothered to learn their own Church's teachings?  Why don't they start with the Sacrament of Marriage?

Once again, and I hate to sound like I'm beating out the same beat on the same drum over and over, if you are Catholic, you owe it to yourself to find a Latin Mass somewhere close to where you are, and start attending it.  Come see the Church as it should be.