Allowed and rejected

Hello Rabbi. I know that in the Rabbi’s opinion, the question of whether Pikuach Nefesh is permitted on Shabbat or rejected Shabbat is without merit. What about permitted and rejected in other matters? For example, a person who rejects a person does not do so, a brother’s wife in a bivum, a mitzvah death, and relatives of a priest?
And could this investigation have any meaning without any merit?
thanks