>Do think this is the issue?
no.
my *absolute guess* would be somewhere there’s

add_action(‘wp_ajax_xyz’, array($this, ‘abc’));
and it’s missing the additional
add_action(‘wp_ajax_norpiv_xyz’, array($this, ‘abc’));

if it works when logged in but not when logged out, my guess would be there something somewhere is missing the right ajax privileges.

you probably want to do the following on a test install somewhere:
the only way to find out what / where is the problem is this

switch to a default theme (like 2016 or so)
disable *all* plugins except the wppizza plugins . (it will look funny, but the functionailty will still be there – just put the cart widget into a sidebar again)
if it works when logged out , re-enable plugins one by one (you will have to log in and log out again after enabling – or use different browser where you do your admin adjustments)

and see which one stops this from working

if it does not work with all other plugins turned off (except wppizza plugins) and the 2016 theme
let me know and i’ll have a look again