You can remove the periods from a copy before testing (with tr/.//d), or else construct a regex with optional periods:

my $to_match = 'xyz123abc';
$to_match = join '\.*', map {quotemeta} split //, $to_match;
# $to_match is now 'x\.*y\.*z\.*1\.*2\.*3\.*a\.*b\.*c'.

$to_match = qr/$to_match/;

/$to_match/ && print for <>;
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The quotemeta mapping is to escape any regex metacharacters which may be in $to_match. There are none in the example.