What separates those who are fluid in their beliefs from those who have rigid views? What causes someone to embrace a particular ideology even when it is not pragmatic and leads to harm? How does one determine the degree to which a belief should be held inflexibly and when it is open to more subjective interpretation?
In cognitive function terms, you may be talking about the difference between introverted thinking or feeling and extroverted thinking or feelings. As introverted functions are more personalised, they are more flexible. Extroverted functions are working according to external (or "objective") rules - although, of course, nothing is ever actually objective but it seems that way to the user.
So if you use Fe/Ti you may have rigid morals that do not flex easily to allow for justification or excuses should someone break the rules. There are a set of rules and you must follow them. If you do not you are selfish. That is the way Fe thinks.
However, Ti internalises data and makes a personal decision that is changeable. It looks for inconsistency and gets to the root. Someone with high Fe and low Ti may say "they shouldn't have done that" basing their ideas on external rules - that is bad, they shouldn't have done that. OR it could say "this person does and says the right things so they can't be all bad". Ti is both more critical and more forgiving because, in combination with Fe, it excludes any "irrelevant" data. So if a person has does and says all the right things but Ni/Fe says that they have bad intentions, Ti cancels out all of those good things they said and did and says the important bit is there intentions. This works the other way round. A person is selfish or makes a mistake that hurts another person. Fe notices it. Using Ni, Ti gets to the core and seeks to identify intentions. This is the important bit. If intentions were good, it cancels out irrelevant data - bad things they have done and said, and classifies the person as "good".
Fe has moral rigidity, but Ti helps it make exceptions.
Let's say that it's about an issue but not a person. An issue that may seem impersonal.
If a person is rigid in their beliefs despite outside evidence or obvious incongruity, it may be that they don't use Ti. Ti hates inconsistency. If a belief simply does not fit into experience of the world or an unconscious picture of reality, it is wrong. For this reason, Ti is both changeable and inflexible. If an idea does not fit with their worldview, it is chucked out. If an idea does not seem inconsistent with their worldview and what "feels right" then it is accepted, even if it appears to in opposition with the person's beliefs. The user can put the new idea into the big picture and this alters the picture itself - same picture altered slightly, sometimes bringing about new meaning.
Te gets its thoughts from the outside world. It may not question what it is told. Like Fe, it has a rigid structure. So if you are using Te you look for "objective" evidence. While a Ti user may say "these statistics don't seem right because that's not my experience - that "feels" wrong", a Te user may says "let's rely on the data". It is a more impersonal belief system. The Te user does not say "this feel wrong or right", or not as much as a Ti user. It trusts details more than Ti, it trusts external data more than Ti.
So Fe and Te can have rigid beliefs because they are externally sourced. Fi and Ti attempts to fit data into a personalised system. The personalised system does have its own rigidity, it is not totally flexible, but seeing as it is not anchored outside of the person, it can be changed.