I don't believe in anything being beyond question or off-limits to questioning. Allowing for anything to be questioned is one way to ensure that a view is true, that it can withstand scrutiny, etc. If the view is true, then it will likely be able to withstand scrutiny.

However, in my many years of debate on various issues, I've come encountered unquestionable mentality when it comes to these views:

Religious views:
- Monogamous marriage (I've challenged this view by showing that polygamy was approved by God, yet some Christian circles don't want to even touch it)
- Religious exclusivism (the view that only one religion is true)
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Secular views:
- Materialism, esp. when it comes to consciousness
- Some LGBT views
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More to be added. Feel free to contribute. What views have you encountered that tends to bring up the unquestionable attitude?