Originally Posted by macropod

Cross-references and hyperlinks are two entirely different things.

By default, cross-references adopt the formatting of the paragraph into which they're inserted. Hyperlinks, on the other hand, ordinarily adopt the hyperlink Style.

Just as you can insert a cross-reference to a heading, bookmark, etc., you can do the same with hyperlinks. That will get you the hyperlink formatting; the downside is that the hyperlink display text doesn't auto-update to reflect changes in whatever it's linked to. The alternative is to apply the hyperlink Style to your cross-references, so they look like hyperlinks (they still won't change colour when followed, though).