When the custom post type or an invoice is being saved after a user subscribes in the front-end, the custom post type is not persisted to the database causing the plugin not to work as expected.
Invoice custom post type saved and normal process of completing registration continues
Thank you for reporting this bug.
It's marked as backlog, so it appears in the to do-list of our development team. You can also contact the developer of the plugin and they can also create a PR if the issue can be fixed in our plugin.
I also get the following PHP error when I try to sign up for the membership:

Hello @benvaassen,
Thank you for the response. I am currently working on the plugin at WPMU Dev. I will try and see if I can add a workaround for this. The error in the logs you shared seem to be a php config and can be adjusted by increasing the value of xdebug.max_nesting_level .
Hey there @benvaassen,
Hope you are well today. I've found that setting the invoice custom post type to private removes this error. I'm still running a few tests but it seems to be working
I confirm, in membershipappmodelclass-ms-model-invoice.php, line 327 put public to false 馃憤
'public' => false,
As this issue is more than 2 years old and has not received any endorsements in the meantime, I'll be closing it. If this issue is still relevant today, please open a new issue thread with new details.
Most helpful comment
I confirm, in membershipappmodelclass-ms-model-invoice.php, line 327 put public to false 馃憤
'public' => false,