(NB: It's not really necessary to post a reeeeealy looooong string to convince us you're dealing with long strings. We're prepared to take your word. Shorter example strings would seem to have been sufficient.)

Insofar as I understand your problem, this is the classic, idiomatic Perlish solution. (I don't know if you really need your  $str1 string transformed also; I do it essentially to support the example.) This approach assumes that  $s1 and  $s2 are always the same length, and also that the null character  \x00 is never a valid part of the  $s1 or  $s2 string.

c:\@Work\Perl\monks>perl -wMstrict -le
"my $s1 = '---DAAAGLRG--G--G-P-LT-IGGY';
 my $s2 = '...XXXXXXXX..X..X.X.XX.X..X';
 print qq{'$s1'};
 print qq{'$s2'};
 ;;
 (my $mask = $s1) =~ tr{-\x00-,.-\xff}{\x00\xff};
 my $t1 = $s1 & $mask;
 my $t2 = $s2 & $mask;
 $t1 =~ tr{\x00}''d;
 $t2 =~ tr{\x00}''d;
 ;;
 print qq{'$t1'};
 print qq{'$t2'};
"
'---DAAAGLRG--G--G-P-LT-IGGY'
'...XXXXXXXX..X..X.X.XX.X..X'
'DAAAGLRGGGPLTIGGY'
'XXXXXXXXXXXXXX..X'
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Update: Replaced  s/// with  tr/// in masked character removal step:  $t1 =~ tr{\x00}''d; instead of  $t1 =~ s{ \x00+ }''xmsg;