I don't think that is the point at all. To that end lies madness.
Showing "them" would be pure social validation and, according to your parent, not recommended. Showing "that" would be sanity protection, just as you understand it.
Feynman is clearly saying disregard others while you are doing the work, not disregard others when you present it for feedback and criticism. That is the spirit with which I responded.
As a developer, there is a third option where your work is simply ignored. If it is functional for you and you are satisfied with your own work, then sure, feel free to disregard others lack of interest, like an artist who values their own work but meets a deafening silence. But please don't disregard serious criticism.