Hi,
Thanks for using our plugin. I can help point you in the right direction.
It maybe possible to use the social login, but you may have to do some customization.
If you follow our themer’s guide:
https://theeventscalendar.com/knowledgebase/themers-guide/
You could move the main Community Templates and add a logged in check before ours and then use the WooCommerce Social Login for the form.
Not sure how their plugin works so there is not much else I can provide on that, but let me know if you have any follow up questions.
Thanks