Why not something like this:

$re = qr{
   \<
   (?:
      (?> [^<>]+ )    # Non-parens without backtracking
    |
      (??{ $re })     # Group with matching parens
   )*
   \>
}x;

$s = "B<I<U<bold underlined text>>> and B<bold text>";

1 while $s =~ s{([BUI])<([^<>]*(?:$re[^<>]*)*)>}{<$1>$2</$1>}g;

print $s,"\n";
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