Best solution for centralised user management system for multiple systems

Your desires [correct me if I'm wrong]:

• You have two apps that are essentially separate things.
• These apps can be served from a web page via HTTP, and either don'thave an auth system or need one revamped.
• You want a centralized login system with social auth.
• You have a single business entity.
• You want a single, combined source of data for e-commerce.
• You are essentially setting this up from scratch on the WordPressbackend side, there is no current mixed ecosystem of users.

My thoughts:You DO NOT want LDAP or Kerberos. Those solutions are much too complex for this situation.You want a SINGLE WordPress install. You can easily setup the backend to answer to multiple domains. In other words a single wordpress install can handle pages at "domain1.com" and "domain2.com" and render the pages with compleately different headers and text to make them APPEAR as two sites. There is no reason to maintain two separate lists of users, because you want a single system to login. Differentiate the users based on their business data, i.e. user1 has data "registered on SiteA", user2 had data "registered on SiteB" etc.

You can place your app into a WordPress page, then use is_user_logged_in() to firewall it behind WordPress. This is an industry standard method of auth and extremely secure if setup correctly. Or if it's a data api, you can place it as an endpoint and leverage the exact same auth system.

Any of the major social auth plugins that are popular in the free .org repo should work out the box with this method.

If you are going to associate blogging, that is, many "posts" about the products, and you want those blogs to be different ecosystems, with different sets of users, you are looking for WordPress Multi-Site. I don't think this is what you want. You don't sound like you are going to "blog". Or at least every page is going to be meticulously curated on these combined sites. So you're probably looking for just a single install to serve content to two domains. NOT MULTISITE.

You should use WooCommerce, simply because it is the most widely supported platform. Setup is 100% free.

You can easily serve pages that are branded totally differently, even in one install. For instance, one WordPress site can serve pages to two domains, and put different logos and headers on the top of the page to make them appear different. One physical machine can serve two domains.

Bottom line: You want a single WordPress setup on a single machine, serving two domains. The content and appearance on the domains can be different at will. Use any popular social auth plugins in the .org repo to firewall the apps.