Yes, sensibilities can be insensible.
My dictionary has two definitions of sensibilities; 1. our responsiveness to anything emotional; 2. our delicate sensitivity. Either way, they are not based on reasons, they are based on our emotions… and our emotions can suck.
With that in mind, it is reasonable to believe our sensibilities can be insensible.
How do you know yours are sensible or not? Just take a look at the things you are emotionally reacting to.
Do they offend you because they are actually harmful to you and your fellow human beings? Or do they offend you simply because you personally don’t like them?
Hate speech, incitement of violence, conspiracies about specific individuals or groups, corporal punishments on children, LGBT+ conversion therapy, anti-vaxxer beliefs, platforming bigots and conspiracy “theorists” without holding them accountable, toxic masculinity and femininity, religious fundamentalism. Those things are harmful because they either directly inflict physical and/or psychological harms upon others, empower others to do the same or compel them to inflict harms upon themselves. If you are a truly decent human being, they should offend you greatly.
But, things like disobeying dress codes, dressing like a slob, speaking with crude accents or dialects, having different tastes, diets and religions, not masculine or feminine enough, too masculine or feminine, being physically unattractive? How are any of those harmful in any ways?
If they do not inflict any physical and psychological traumas upon anyone, if being offended is the only thing you and others experience, then they are definitely harmless and your sensibilities are definitely insensible.
Obviously, we are human beings. No one has the right to tell us how and what to feel. No one has the right to prohibit us from establishing our own standards, no matter how arbitrary they are.
But, it becomes a problem when you mistake your emotions as objective measurement tools, when you are unable to distinguish your biases from the objective reality.
In this case, you and your sensibilities can go fuck yourselves.
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