Hi Paul
Change the CSS you posted above to this:
.blog .entry-meta,
.blog .entry-content,
.blog .entry-footer .cat-links,
.archive .entry-meta,
.archive .entry-content,
.archive .entry-footer .cat-links {
display: none;
}This will hide the categories in the entry footer (instead of hiding all of the entry footer) so the tags will still be displayed.