You can use is_category to check if the category is “members” and then load the appropriate template.
In get_template_part() use the template name for the second parameter instead of get_post_format().
In this example your template should be named “content-members.php.”
while ( have_posts() ) : the_post();
if ( is_category( 'members' ) ) {
get_template_part( 'content', 'members' );
} else {
get_template_part( 'content', get_post_format() );
}
endwhile;