In this post I combine my own thoughts with those explained in Nicholas Rescher's book: Philosophical reasoning (highly recommend it btw).
The definition of conjecture is:
an opinion or conclusion formed on the basis of incomplete information.
"conjectures about the newcomer were many and varied"
Clearly, we would find the claims of astrology, divination, new age woo, and the like to be based on nothing but conjecture. The conclusion that the stars have an influence on the machinations of human society is not supported by any statistical evidence, for example.
No scientific theory can be seen as ultimate - there are no non-negotiable, perennial "facts" surrounding scientific inquiry. What is the case today may not be the case tomorrow, or what is seen today as the most plausible theory may be contradicted tomorrow. Without a complete knowledge of all the information and the knowledge that one knows all the information, no theory cannot fail to not be conjectural.
Philosophical theories are also conjectural, probably even more so than most scientific theories but less so than pseudo-scientific theories. The fact that we cannot find more information via the empirical route means that a question is largely non-empirical and thus non-scientific. (of course this is a useful simplification).
Thus, any process of inquiry is going to have to settle with the next-best option: truth estimation.
But why would someone desire to believe in an estimation, a mere approximation? The only answer (which is of course approximating) is that beliefs are useful. We can see how we ought to believe in the claims of astrologers or diviners because there is very little evidence for their claims and we don't have time to waste on their bullshit.
If we're engineers, it will be useful to believe that the laws of physics apply everywhere. If we're organizing a political entity, it will be useful to know of various political philosophies so we can pick the best one, the one that does the job better than all the others. If we're trying to figure out what to do in a situation, ethics will come into play.
But when it comes to the more theoretical scientific and philosophical questions (especially metaphysical questions), there seems to be very little necessity to believe in anything. Whyshould I believe in strings, or quarks, or the Big Bang? Why should I believe in universals (or perhaps tropes), or the mental (or lack thereof), or God(s)? Since any belief we have will ultimately be conjectural, and these theoretical conjectures have little to no usefulness to my daily activities, why should I host any of these beliefs?
The answer (once again an approximation), I think, is that although answers to these questions are not practically useful, we nevertheless need them. We are curious explorers who know the possibility of being wrong but set sail regardless.
To the uber-skeptic, this is unacceptable. They will contend that any non-useful conjecture is not worth believing or not even worth pursuing refinement at all.
Unfortunately, what this uber-skeptic gains in the lack of erroneous commissions, she loses in omissions. The uber-skeptic is so engrossed with being wrong that she never even tries.
Similarly, the highly-gullible sacrifice level-headedness for the commission of silly beliefs.
Philosophical questions can be categorized into three different kinds:
Informative (what is the case)
Practical (how to do things)
Evaluative (what to aim at)
The latter two (practical and evaluative) are the philosophical questions whose conjectures are necessary for survival and prospering. The first one (informative) are the more theoretical questions, the questions who have very little to no immediate impact on the day-to-day. As such, there are very little consequences of being right or wrong, either.
It stands, then, that any belief we have is subject to revision, updates, or expulsion. Dogma is the death of reason and leads to an over-confidence in a belief that is nevertheless conjectural. To force someone to believe something that is neither practical or evaluative is an infringement on their epistemological liberty.
But for the rest of us - those who are genuinely interesting in understanding and appreciating what can be intelligibly communicated - full speed ahead.