WRT secondary sources (previous post), I don't want you to think I have no standards. I try not to make authors from the past say things they are not saying. When one has a large storehouse to draw from, the temptation is there to pull a particular quote of Martin Luther's and bend it into service for what you are trying to prove, even if you know that was not his intent. In the same way that "Taking the Lord's Name in vain" means forging God's signature under your ideas, Dickens or Shakespeare can be pressed into service as pretended authorities supporting your plan for government or marriage advice.
I think I used to do that with some conscious dishonesty in college, and maybe later. I may not have gone so far as making Christopher Marlowe say things I knew he would likely disapprove of, but I was certainly careless, with a very long kite string of what I thought he might mean, based on no information whatsoever, because it would be so cool if Marlowe had actually said something like that - and prove my little theory about whatever. People more often use vagueness, saying "Well, in the Middle-Ages, people believed that..." It's hard to disprove.
Knowing it is a dishonesty I was prone to, I try to be very strict with myself about such things now. Once one gets strict about it, noticing where the little cheats are likely to hide, one can't help but notice when others are doing it.
One does not have to be dishonest at all, and the carelessness might not be immediately apparent. It may be the person you are reading whose research is sloppy - or dishonest, and your fault is that you are accepting too readily because you so want the idea to be true. I am reminded by Scott Siskind's caution about new treatments, which I quoted about a month ago
"This is a very pre-replication-crisis book. In these more cynical days, we know that the first few studies on any technique – usually done in an atmosphere of frothy excitement, by the technique’s most fervent early adapters – are always highly positive. And later studies – done in an atmosphere of boredom, by large multi-center consortia – are almost always disappointing."
So too with new research about many things. To make up an example out of whole cloth, if someone suggested that several early Gnostic sects in 1st C Mediterranean cultures gave a much more elevated status for women, and that was (really) why their Christology was rejected, that idea would be popular in some circles. It would not only be popular with women keeping up with theology these days, but with anyone who thinks the Gnostics got short shrift in the early church for accidental reasons, not the Holy Spirit, or wants to kick the early church as having gotten it all wrong for emotional or intellectual loyalties of their own (such as homosexuality, for example), and even people not particularly interested in the church at all, but with agendas about women or homosexuality or pacifism or whatever. Whether the theory was true or not, and whether there was much evidence for it, it just might become settled doctrine among those groups and prove impossible to kill. We already have examples of people believing things about history because wouldn't it be cool if...rather than actual evidence.
I know of no solution other than personal vigilance. It is another long-standing theme of this blog, that I hope outlives me long after I have died, to regard that which you wish to be true should be treated with heightened suspicion. A new study has come out about Covid and masks. Quickly: what do you hope is true? A high-ranking defector from Iran spills his guts. If what he says is devastating to Trump's policies do you reconsider what you have been thinking, or do you immediately revert to "this guy is not a real defector, he is a plant from the Iranian government which wants us to think the opposite?"
I will repeat the related sermon I often preach: this tendency to see what we want to is not a function of intelligence, of knowledge, or of training (unless you had that rare training that focused on humiliating you to teach you to drop your preconceived notions, as CS Lewis got from WT Kirkpatrick before entering Oxford), but of your personality, approach, cast of mind. If you know a great deal about a subject you are in all likelihood more susceptible to the fashions of the school within your discipline, or the year in which you graduated from the Naval Academy, or consensus of everyone at your agency.
The more you know about a subject, the more easily you can beat down the legitimate challenges to the conventional wisdom by observant outsiders. Yes, many of these outsiders will be simply fools who know nothing, and that will sucker you into thinking you can take on all comers. I have done that with mental health, history, basic theology, and a dozen other subjects over my lifetime. You know something, and keep encountering knuckleheads who make the same assertions you have been hearing since you were twenty, that have been utterly demolished a hundred times. But there will also be people whose knowledge has strong overlap with yours, of neurologists commenting on psychology (or vice versa, and in all following cases), or historians on criminology, or small business owners on nonprofits.