[SalesForce] Conditional lightning components rendering in community

There is a domain related issue that we are working on that is Community specific. We have fixed this in Spring'16 already and are evaluating backporting the fix to Winter'16 patch.

Related post Lightning Out for Visual Force in a community works in dev org but fails in sandbox

I assume that by providing a custom page/experience to the user you are using a lightning component to do so. If that is the case, you are likely to have an underlying apex service that fetches some user-specific data. If you have an apex class you can use the UserInfo.gertUserId() to get the running users Id and from there you can retrieve more information about the user.

If you don't want to use apex, you can use this javascript snippet in your controller to get the user id:

var userId = $A.get("$SObjectType.CurrentUser.Id");
Console.log(userId);

With that id, you can use the lightning data service to retrieve user-specific parameters.

The very last option I can think of is to build page variations for your home page and assign them to different profiles. This will not make it 100% unique for each user but allows you to tailor the experience to user groups.