You make great points, especially the fact that people are often pushing some kind of bias. However, there definitely is a skill to determining the reliability of a source, it’s called Information Literacy. You’re also right that each person has to develop this skill for themselves.

For those who truly want to strengthen their Information Literacy, I’d recommend starting by learning to recognize various common cognitive biases and logical fallacies. Simply being familiar with how these things work gives you a leg up on identifying nonsense, even if you can’t recall the exact name of the bias or fallacy that may be occurring.

Skepticism will get you far in determining accurate from inaccurate, and it’s important to apply it universally - question everything - instead of simply applying skepticism toward things you don’t like. Similarly, be open to changing your mind when presented with new information, because the more you learn how to see through the misinformation, the more you may find the world around you is different from what you’d been told.