Hello,
Sorry for the delay in response.
We have tested the synchronization of buddy press with WCMp and it is working fine at our end as you can see here (https://www.loom.com/share/bb5afaf6f3ca484aba229ec7f939db9d)
It seems to be some theme/ plugin conflict. May I know if you have checked marketplace plugin with WooCommerce and standard theme (storefront/twenty). Please deactivate all your plugin, except WooCommerce and WCMp + addon. You can then check the flow. If everything is working fine, in order to detect which plugin is causing conflict- please activate each plugin consecutively and check the flow.
Similarly, for theme conflict- please deactivate the current theme and check with standard WooCommerce theme (storefront/twenty) It is suggested to please perform these tests on your staging website and keep us posted with the outcome.