in reply to Why does /i not seem to work

You can try this: say $rx to see what $rx is actually interpreted as. Spoiler, you'll see this:(?^u:abc|xyz).

As documented in Extended Patterns:

Starting in Perl 5.14, a "^" (caret or circumflex accent) immediately after the "?" is a shorthand equivalent to d-imnsx. Flags (except "d") may follow the caret to override it. But a minus sign is not legal with it.
The ^ actually disables case insensitivity. That's because the qr operator "remembers" the flags used when creating a value with it, so that you can use it to always mean the same thing, regardless of where it's used.

Three ways to solve your issue, use the /i when creating $rx: $rx=qr/$rx/i;. Use lc like you already did. Or do not use qr and keep the regex as a string.
But that last one has some disavantages, using qr// will tell you if your regex is invalid sooner (if you use the regex in a completely different place, you might want the error message to be close to the definition, not the use), and it's not a bad thing to have something that is meant to be used as a regex to have the "type" Regexp.

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Re^2: Why does /i not seem to work
by AnomalousMonk (Archbishop) on Nov 21, 2019 at 16:14 UTC
    ... keep the regex as a string ... has some disavantages ...

    Not least of which is that a Regexp object interpolates into another regex as an independent, quantifiable non-capturing group, and an interpolated string does not: 

    c:\@Work\Perl\monks>perl -wMstrict -le
"my $rs =   'abc|xyz';
 my $rx = qr(abc|xyz);
 ;;
 my $regex = qr( $rs+ $rx+ )x;
 print $regex;
"
(?x-ism: abc|xyz+ (?-xism:abc|xyz)+ )

    [download]
    The two different representations can have very different effects when interpolated into a larger regex.

    Give a man a fish:  <%-{-{-{-<

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