This should work as long as you don't care about retaining empty strings (<tag> </tag>) and as long as the content itself doesn't contain the < character. A good XML parser will of course also work, but if your data is simple, there may be no need.

use strict;
use warnings;

my $xml = join '', <DATA>;
while ($xml =~ s/(<\/?.*?>)\s+(<\/?.*?>)/$1$2/sg) {}
print $xml;

__DATA__
<outermost>
    <innermost>
        <first>1</first>
        <second/>
        <third>These spaces are to be preserved.</third>
    </innermost>
</outermost>
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