Modal Registration not submitting data

It sounds like the two plugins are not compatible, but you’d need to check with the plugin authors to be sure. Go to each plugin’s dedicated support forum to confirm.

The modal plugin is likely assuming only the standard login fields exist. It’s impractical to know what other fields might be added by other plugins because they could be added through a number of different methods and there is no way to know what that might be.

You could hack the modal plugin to present additional fields. This would be a major departure, so you cannot expect help from the author any more. You need to rename the plugin so your edits do not get overwritten. It would be your responsibility to review plugin updates for any important changes you need to incorporate into your modified plugin.