を問（と）わず is a pattern which makes use of the special-class う-Verb 問（と）う ‘to inquire’ and the literary auxiliary verb ず, which connects with verbs in the same way, and carries the same meaning as ない. While the literal meaning of this grammar structure is ‘without questioning (A), (B)’, it is used more as a formal way to express ‘regardless of (A), (B)’, ‘whether (A) or not, (B)’, or ‘with or without (A)’, (B)’.
This structure is seen almost exclusively after nouns, but can also follow structures like か, or かどうか that are modifying adjectives. を will mark the ‘question’ which is ‘not being asked’.
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宗教（しゅうきょう）や国籍（こくせき）を問（と）わず、このイベントには誰（だれ）でも参加（さんか）できます。
Everyone is welcome to attend this event, regardless of religion or nationality.
パソコンの上級者（じょうきゅうしゃ）か初心者（しょしんしゃ）かを問（と）わず、初（はじ）めてこのサービスをお使（つか）いになられる方（かた）には初心者（しょしんしゃ）コースから始（はじ）めてもらいます。
Whether you are an advanced computer user or a beginner, we ask first-time users of this service to start with the beginner course.
このマンションを買（か）うかどうかを問（と）わず、この物件（ぶっけん）を押（お）さえたい場合（ばあい）は手付金（てつけきん）を払（はら）ってください。
If you want to hold on to this property, whether you buy this apartment or not, you must pay a deposit.
Occasionally, は will replace を at the beginning of 問わず. This puts further emphasis on contrast, and slightly strengthens the phrase overall.
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どのブランドかは問（と）わず、とにかく新（あたら）しい靴（くつ）が欲（ほ）しいです。
I just want a new pair of shoes, regardless of which brand.
Caution - Although
を問（と）わず may be thought of as similar to ‘regardless’, there are actually situations where the nuance is closer to ‘in any case for (A), (B)’. This is particularly true when (A) is being expressed as a scope. Let’s compare
を問（と）わず to
に関（かか）わらず to see the difference.
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彼（かれ）は昼夜（ちゅうや）を問（と）わず、ずっと働（はたら）いている。
Whether it is day or night, he is always working.
彼（かれ）は昼夜（ちゅうや）に関（かか）わらず、ずっと働（はたら）いている。
Regardless of day or night, he is always working.