The class of non uppercase English characters is [^A-Z]. So you need

$str =~ /^A[^A-Z]*B[^A-Z]*C[^A-Z]*D$/;
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You can write this a little more clearly as:

my $nu = qr/[^A-Z]*/;
$str =~ /^ A ${nu} B ${nu} C ${nu} D $/x;
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(Use [:^upper:] or the Unicode \P{IsUpper} for non-English text.)