last but not least

  DB<171> $str=$str0
 => " bla0 \"ignore a1\" bla1 \"ignore a2\" bla2"

  DB<172> @parts=split '"',$str
 => (" bla0 ", "ignore a1", " bla1 ", "ignore a2", " bla2")

  DB<173> map {s/a/A/ unless $x++%2} @parts
 => (1, 1, 1, 1, 1)

  DB<174> $str=join '"',@parts
 => " blA0 \"ignore a1\" blA1 \"ignore a2\" blA2"
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also as one-liner

  DB<185> $x=0;$str=$str0
 => " bla0 \"ignore a1\" bla1 \"ignore a2\" bla2"

  DB<186> $str= join '"', map {s/a/A/ unless $x++%2;$_} split '"', $st
+r
 => " blA0 \"ignore a1\" blA1 \"ignore a2\" blA2"
[download]