my @lst = qw( A,G AG,CT TC,CA GAT,CGA CGAT,TG ,G
  ACGT X,A AA,G AC,GGC ATGA,TGG ATCXG,AAC ATA,TG GTA,YC);

for (@lst) {
    my $good = do {
        m/^ [ATCG]+ , [ATCG]+ $/x
          and not grep m/(.) .* \1/x, split ',';
    };
    print $_, $good ? ' good' : ' bad', "\n";
}

##</code><code>##

A,G good
AG,CT good
TC,CA good
GAT,CGA good
CGAT,TG good
,G bad
ACGT bad
X,A bad
AA,G bad
AC,GGC bad
ATGA,TGG bad
ATCXG,AAC bad
ATA,TG bad
GTA,YC bad