I think you’ll need to put the rules in a different order... and adjust them a bit... try this:
RewriteBase /
RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]
RewriteRule ^product/category/(.*)$ product/category?tags=$1 [L,QSA]
And I suspect you’ll need that "QSA" for "query string append"... really the authority here is the apache docs.
it’s a bit tricky to have this happen in one .htaccess file... if I were you I might try creating a dummy "category" directory with a dummy "category" file in there, and putting a separate .htaccess file in there, just to make sure that the rules from the main .htaccess file didn’t interfere...