if (s/^FOO =\s//){
    s/\\$//;
    push @array, $_;
}
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Basically, the only real change for efficiency is to do the replace once instead of twice. The rest is style, though style counts. I might suggest, though, making the first one a bit less strict, something like

if (s/^FOO\s*=\s*//){
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So it doesn't matter if there's more than one space, or a tab, or...whatever. But that's for your code to do with as it will.