I good translation I use is
にかかわらず - Regardless of
にもかかわらず - In spite of
雨にもかかわらず出かけました。 Similar to なのに
In spite of the rain, I went out.
曜日にかかわらず入ることができます。 Similar to を問わず
Regardless of which day it is, you can enter.
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