At this time I've an outdated URL that's getting 404'd:

It must be rerouted to:

This does not work:

Redirect 301 /category/?tag=blue-example

How do you correctly rewrite this URL?

The mod_alias does only chech the URI path and never the query (the part following the ?). But you should use mod_rewrite with this:

RewriteEngine on
RewriteCond %{QUERY_STRING} =tag=blue-example
RewriteRule ^category/$ [L,R=301]