It's no secret that factions try to hijack Church teaching to either try to give their political platform credibility (if they are similar) or to discredit the Church (if they are opposed). For example, the Church teaching on caring for the poor is hijacked into either equating this teaching as a mandate to vote for a party platform or to indicate that the Church is being biased and therefore should not be heeded.
In America, both parties use both tactics, and some members of the faithful who want to promote a politcal cause will misquote Church teaching a way that makes it appear as if the Church is changing...either to praise the party or discredit the Church by accusing them of "becoming political."
For people who get caught in it, this is nearly an airtight trap. It leads one to either think that fidelity to one political faction is fidelity to the Church, or to claim that they are being faithful to Our Lord or the earlier Church over the Church today.
This happens in two different ways. In one case, we have obvious schizophrenia where the US bishops are simultaneously called left-wing and right-wing by foes of different positions. But a new tactic is emerging, One where both factions react to accounts from the secular (and religiously illiterate) media and ignores what they ignore. As a result, people are ignorant of the fact that Pope Francis is just as firm in defending Catholic moral teaching as his predecessors, and his predecessors were just as firm as Pope Francis on social justice.
For example, I recall a debate on Facebook with a woman who angrily wanted to know why Pope Francis never mentioned the plight of Christians in the Middle East when he spoke about injustice. She was shocked when I produced an address by the Pope pleading for the world to help these Christians and retracted her objection. She literally didn't know the Pope had spoken about this.
People forget that ALL news media is partisan. It's easy to deride "Faux News" or MSNBC, but the entire media is biased. If a person is unaware of this, they will not realize that a distortion IS a distortion.
The remedy for partisanship is to recognize that a political position must be judged by the Church, NOT the other way around. We must remember that deploring abortion is not "right wing" and deploring the treatment of migrants (legal or not) is not "left wing."
I believe that we must change our method of thinking. We must stop assuming that secular reports about Church teaching are accurate. We must first seek to understand what the Church intends to teach. We must reject an arrogant overconfidence in our ability to interpret what we think is the "plain sense" of a document (if I had a dollar for every time someone with a wrong interpretation appealed to the "plain sense" of the document, my student loans would have been paid off years ago). We must realize that our perspective as 21st century Americans (or Europeans etc.) may lead us to interpret words in ways that the Church NEVER intended.
In such a case, the Church is not at fault for "speaking unclearly" (a common charge). Rather WE are at fault for assuming that the Pope is thinking like a 21st century American. It's pretty arrogant to assume our cultural experience is normal.
I believe that, for us Catholics, we must step back from our dualistic political views where Left and Right become Right and Wrong. We must start thinking of the Church as Mother and Teacher again and apply her teachings to the issues of the World. That means rejecting the tendency to view Church teaching as a political platform and accepting the view that all politics need to be re-formed (and thus reformed) by Christian belief that doing good in relation to God, neighbors and self is to be sought and evil rejected. When it comes to the parable of the Pharisee and the Tax Collector, we need to stop thinking like the Pharisee.
It means we must stop thinking of politicians as evil incarnate when they have the "wrong" letter (D or R) after their name and stop making excuses if they have the "right" one. Regardless of your opinions on Hillary Clinton or Donald Trump, we have to think of them as fellow sinners who God wishes to save as much as He wants to save us.
That means when the Pope shows compassion to a person on the "wrong side" of the political divide, we don't assume he is blessing the party platform of our opponents. It also means we don't assume he gives carte blanche endorsement to our political platform when he says something our party agrees with.
What it boils down to is that the Christian must constantly assess themselves, turning away from evil and back to God. It means we must pray that our hidden faults are revealed to us and for the grace to change our ways.
This, I believe, is the remedy to the trap of ideology.