"Based on the authors examples of Trump and vaccines, the author is talking about sympathy and compassion, both of which require of us to take sides."

That's incorrect. There's nothing about either sympathy or compassion that requires taking a side. 

The taking of sides is a strategic act, typically informed by both cognitive and emotional factors. Once a side is chosen, it tends to interfere with normal feelings of empathy and compassion. For example, when a player on the opposing team is injured, you're less likely to feel empathy for him than you would if it was a player on the team you support.

At least from a Buddhist's point of view, compassion can take no side. It's not an emotion. It's a state of being that's given freely to every living thing, without moralizing or politicizing the circumstances. Empathy on the other hand is an emotional connection between you and someone else, typically due to difficult circumstances the other is experiencing.