(A) をよそに (B) is used when someone ignores (A) - advices, objections, expectations, worries of others, and does (B). Often, but not always used for criticism, though it might also express a sense of admiration. In (A), phrases like 心配、不安、反対(の声), 忠告、期待、非難 are often used. 余所（よそ） means “another (unrelated) place” so をよそに lit. means “(to treat) as somewhere unrelated” - “as unrelated matter”. Has the feeling of a written expression.
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