〜によらず
regardless of; despite (appearances)
Noun + によらず · 見かけによらず
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によらず means "without depending on", so "regardless of": 年齢や性別によらず、誰でも参加できる, "anyone can take part, regardless of age or gender".
The noun is a category: age, gender, experience, or 何事 ("everything"). 何事によらず means "in anything, in all things".
The most famous use is with 見かけ ("appearance"): 彼は見かけによらず力持ちだ, "he's strong, despite how he looks". The proverb 人は見かけによらないものだ means "you can't judge a book by its cover".
It's the negative of による (N3's によって, "depending on"), so the puzzle is to check whether the result depends on the noun or not.
Examples
年齢や性別によらず、誰でも参加できる。
Anyone can take part, regardless of age or gender.
彼は見かけによらず、力持ちだ。
He's strong, despite how he looks.
人は見かけによらないものだ。
You can't judge a book by its cover.
何事によらず、基本が大切だ。
In anything you do, the basics are what matter.
経験の有無によらず、応募できます。
You can apply whether or not you have experience.