Ok,
The CLI version works out of the box: /usr/local/bin/php /home/#dir#/public_html/modules/civicrm/bin/cli.php -s #domain# -u #cronuser# -p #cronpwd# -e Job -a execute
The HTTP version needs a change in BackdropCMS .htaccess
.htaccess has this:
# Redirect common PHP files to their new locations.
RewriteCond %{REQUEST_URI} ^(.*)?/(update.php) [OR]
RewriteCond %{REQUEST_URI} ^(.*)?/(install.php) [OR]
RewriteCond %{REQUEST_URI} ^(.*)?/(cron.php)
RewriteCond %{REQUEST_URI} !core
RewriteRule ^ %1/core/%2 [L,QSA,R=301]
If you make it this it works:
# Redirect common PHP files to their new locations.
RewriteCond %{REQUEST_URI} ^(.*)?/(update.php) [OR]
RewriteCond %{REQUEST_URI} ^(.*)?/(install.php) [OR]
RewriteCond %{REQUEST_URI} ^(.*)?/(cron.php)
RewriteCond %{REQUEST_URI} !core
RewriteCond %{REQUEST_URI} !civicrm
RewriteRule ^ %1/core/%2 [L,QSA,R=301]
Going to ask for a change of default .htaccess in BackdropCMS
--
update: This is now part of BackdropCMS core, although made slightly more generic:
RewriteCond %{REQUEST_URI} !modules
is added to .htaccess