Could it be that $variable contains text and not a regexp pattern? Fix:

my $sep_re = quotemeta($sep);

my @fields = split(/$sep_re/, $_);
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or

my @fields = split(/\Q$sep/, $_);
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For example,

$\ = "\n";
$, = ";";
for my $sep (",", "\t", "|") {
   my $line = join($sep, qw( a b c ));
   print $line;
   my @fields = split(/\Q$sep/, $line);
   print @fields;
   print '';
}
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a,b,c
a;b;c

a       b       c
a;b;c

a|b|c
a;b;c
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Or maybe you are trying to split on the two characters "\" and "t" instead of an actual tab character?

$\ = "\n";
$, = ";";
for my $sep ('\t', "\t") {
   print split(/\Q$sep/, "foo\tbar\\tbaz");
}
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foo     bar;baz
foo;bar\tbaz
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