> It’s really hard to be a Catholic, or a Christian, and not lean left.

I would be careful here. You are operating under a very peculiar view of left/right (not a very accurate view in my estimation). Left/right are generally labels of little value apart from particular time and place.

> at the core of Christian faith lies the notion of equality

Equality only as persons or in dignity, yes, but Christianity/Catholicism is anything but egalitarian. The distribution of qualities, both inherent and cultivated, is unequal. As Chesterton wrote IIRC, this latter sort of egalitarianism is the equality of envy and cutting down. Whereas an envious elitist may try to outdo his opponent, the egalitarian will deny or cut him down. Those are pride and envy, both mortal sins and therefore surefire ways to temporal disorder and the eternal self-destruction known as Hell.

> forgiveness and understanding the other

The coupling of these two seems to suggest that what is forgiven is understandable or resolved by understanding. But that is not true forgiveness. If someone were to wrong me in some grievous way, out of ill will, I should feel the proportionate degree of anger. Just as wrath, inordinate anger, is a defect, so is an absence of proportional anger. Anger moves us toward justice and its absence at times when it is needed encourages the continuation of evil since the trespasser is never sent a clear signal that his actions are evil. We forgive not because "it's okay", but because what has been done isn't! We want the contrition of the trespasser. And forgiveness does not rule out the need for justice. We may show mercy, but that is left to prudential judgement. Charity is totally subject to the truth. To quote St. Pius X, the "primary duty of charity does not lie in toleration of false ideas".

> as well as loving everyone, even those who do not reciprocate.

Love here is the love of willing the objective good of the other, not the sentimental ersatz variety commonly espoused today that rests on feelings. What is an enemy? Someone who is ill willed. We do not love him in any human way. We love him for his sake as an act of charity, for his conversion and repentance. Man's ultimate fulfillment is to know and love God, the supreme and inexhaustible cause, cause of causes. Good brings us into better alignment with that infinite and highest of goods, evil takes us away (though we are incapable of reconciling ourselves to that highest good on our own, hence the sacraments and grace).

You might find this post more informative than what I have written[0]. But to sum things us: Christianity/Catholicism is anything but the Church of Being A Nice Fellow. The military language (spiritual warfare, spiritual combat, the Church Militant here on earth, talk of spiritual battle in St. Michael's Prayer) in the Tradition are not a mistake. You just have to understand what the battle is all about. Read the New Testament and you don't get a picture of a Nice Jesus, only a charitable one. Nice people don't tell others that if they keep heading where they're heading, living in the way they're living, they'll not only end up miserable, but they'll end up in Hell. Nice people don't throw money changers out of the temple. Nice people don't speak truth to power. No, only loving people do that.

[0] https://edwardfeser.blogspot.com/2019/11/against-candy-ass-c...