Plugin Using get_the_content Causing Issues With Tag

The logical fork between displaying full content and teaser (that’s what part from start of post to more tag is called) is ruled by $more global variable. Which depends on other global stuff and so on, important point being it’s not set to 0 when you want it to be. Likely because you are running this in context when it wouldn’t be set to zero for normal loop either.

Something like this should work:

add_filter( 'woothemes_our_team_content', function () {
    global $more;
    $real_more = $more;
    $more      = 0;
    $output    = wpautop( get_the_content() );
    $more      = $real_more;

    return $output;
} );

You can just work with link there, or hook into the_content_more_link to customize it.