There is a cost to evidence + belief combinations. This is to say, although certain evidence can be interpreted away with certain beliefs, there is an epistemic cost to doing so – it becomes less plausible.
When people get to a certain point, they can look at another belief set, to see which belief set has less epistemic cost to it – which is more plausible.
Once the evidence + belief epistemic cost outweighs some alternate, we can say a person arrives at an evidentiary threshold.
Needless to say, various non-epistemic factors affect people’s evidentiary thresholds – for example, they might have money or status tied to a certain belief being true, and so dishonestly downplay certain evidence.
In one’s own case, if one is interested in the truth, one ought to weight things accordingly, as it is easy to allow these factors to influence our own decisions.
Evidentiary thresholds can be galvanic. They can push one to find more or different evidence, hence changing the equation, or push one to carefully review implicit or explicit beliefs related to the evidence, to see if there is something wrong there.