Do we have a sense of our tendency to "Both-And"?
And do we therefore actively work to maintain our sense of "stability"?
Research suggests a definite Maybe.
This is from the American Psychological Association (I've bolded key bits for you skimmers ;-):
We swim in a sea of information, but filter out most of what we see or hear. New analysis of data from dozens of studies sheds new light on how we choose what we do and do not hear. The study found that while people tend to avoid information that contradicts what they already think or believe, certain factors can cause them to seek out, or at least consider, other points of view.