Service order

Nope, it is not possible through the admin UI, only using custom hook_form_alter to change widget settings.

Thanks
AndyB

This feature is implemented in 7.x-1.0 as an advanced setting - you can specify a string of providers, separated by commas, and this setting will override checkboxes from the main config tab.

Thanks
AndyB

Nick,

But it's not a user-friendly solution for this moment

I don't have time to implement the user-friendly solution for services order (I mean the drag-and-drop solution in the admin UI). It will require much more coding for the admin UI and will complicate the maintenance efforts.

Much better if the lists of primary and secondary provicers could be the same and site admin can choose which ones he need to turn on.

They are the same. But there is some JavaScript on the admin UI that hides the auth provider from the main list if it is checked in the additional list. Just uncheck the provider in the additional list and it will appear in the main list (uncheked providers will be in the both lists - once you check it in any list it will disappear from the other list).

The big problem now that Google (one most popular) and Yandex aren't present in primary services list!

There is no such problem, hope the above explanation helps with it.

So you can make any providers to be in the main list, but to change its order you need to use the advanced tab and a comma-separated string - shouldn't be too hard, right?

Thanks
AndyB