I think the biggest problem is not that there may be many truths, but that people don't even bother seeking out the best evidence or reasoning against their truths.

To clarify, there are formal truths: widely-accepted hard science, e.g. “2 + 2 = 4”. Technically, there’s a point where we can’t fundamentally prove anything (“if a tree falls and nobody hears it, does it make a sound?”), and rarely we get things wrong (e.g. classical physics)….but in practice, these are true, end of discussion.

Then there are informal truths: e.g. “the Earth is round”, “the sky is blue”, “Gala apples are red”. You can nitpick them (the Earth isn’t a perfect sphere, the sky is only blue during the day in areas without high pollution, Gala apples may be pinkish or have yellow blotches, or exceptional discoloration), endlessly or until they become formal (possibly by becoming self-referential). But in practice, these are also true (like formal truths; although it’s important to know the difference because…)

The problem is, there’s no line between an informal truth and uncertainty/opinion that isn’t true. Like you know ##FF0000 is red and ##00FF00 is not, but there’s no exact color that separates “red” and “not red” (it depends on person, mood, surroundings…) Consequently, unlike formal truths, informal truths have false implications (“fuzzy logic”). An informal truth can be phrased in a “misleading way”, priming the reader for a false implication (a formal truth can be phrased in a convoluted or unintuitive way, but interpreted formally, never leads to a false implication).

The vast majority of discussion is not formal. Even the smartest people constantly fall for false implications. And this isn’t completely solvable, because we fundamentally can’t formally define everything (too much detail): we tried with GOFAI, it failed and its successor, neural networks, informally defines things like us (by forming a lossy model of the world, then generalizing it).

There is only a single source of truth and that is objective reality. Maybe you agree with that, but your wording is messy. It's true that different perspectives can yield their own particular bits of truth, if that's what you're saying.

The problem arises when there are contradictory truths, and defenders of one or both sides refuse to dig deeper to both self-reflect on what they believe to be true, and perhaps come to a deeper more correct understanding.