The sentiment of this question is well placed and makes me happy. We should be suspicious of the colonial archive. But the Archivo General de Indias, the imperial archive in Seville, alone contains approximately 80 million pages of material related to colonial administration and happenings spaced out over five centuries. And that doesn't count the dozens of national archives and hundreds of local, state, and religious archives in the Americas. People sometimes refer to the Spanish empire as an empire of paper. To draw from James Scott, empires "see" through their documents. They are how administrators knew what was going on. In short, we can't accept or dismiss any particular document as inherently reliable or not reliable; every authentic document is potentially useful to answer some questions, and every document has pitfalls--many of which come from the challenging colonial context that led to its creation.

What one must do then is consider each document carefully. Why does this particular document exist? What circumstances informed the perspective of the person who created it? What flaws might it contain? How does this document vibe with other documents about the same event? Do other documents confirm what it says, or challenge it, or provide a different perspective? How do we reconcile the varied views? This is really how historians do research on the colonial period. We learn about the documents, we learn about the wider context using primary and secondary sources, and then we try to put many of those flawed pieces of paper into dialogue with one another to answer larger questions about the past.

In your question, you ask specifically about Jesuit documents. You're exactly right to point out that they would bring a Spanish Catholic lens, which presents a diverse set of perspectives, but also a very narrow set of perspectives about a moment in the past. The first thing we might do is to consider what a 'Spanish Catholic lens' would mean in a particular time period and context. Next, we might ask where specifically these documents were produced. Were these documents produced on the fringes of empire in say Paraguay where the Jesuits were active in famous missions? Or perhaps in an urban center like Lima, where the Jesuits had schools? Perhaps it is some mundane document like a contract or an inventory of goods purchased by the jesuits. What might these show about Jesuit life. After knowing a little bit more about what type of document it is, we might go in from there. For example, what have people said about the Paraguay missions? Who lived in the missions? What else was happening around the missions at the time (slave raids from Brazil perhaps)? What ideas did Jesuits have at the time about indigenous people, colonial administration, about religion, about missionizing that might explain why they were doing the things they were doing? What silences are present in the document (e.g. women just not included)? Whose voices or perspective are not included? If we included these voices, would it change with this particular document teaches us?

All of that questioning help us understand the document and also help us avoid simply accepting what it says at face value. Reading many other documents alongside this one places the author of the document in the world. Then, you must ask what does this document and the world that it was a part of say about the particular questions that I am trying to answer? But even your questions, by virtue of being asked by you in your particular context, shapes the type of history that you write. You will center some narratives and downplay others. You are also unreliable. And that is why history tends to change...or at least the way the story is old changes, even when the source bases end up being basically the same.

So how reliable are colonial documents? Not reliable in and of themselves. No primary sources are though. But documents can be made more reliable with specific methods of contextualization and corroboration.