UPDATE : I was able to use an old phone and tried different old Sonic Dash versions.
I was even able to link the game with an old Google Play version, and it worked !
The game did synchronised with my profile, and I could check my current 40/41 achievements in-game.
But the Facebook button did not work and I couldn't get the 41th one.
When I click on the button, nothing happens.
After installing and reinstalling different versions, to see if I could find a working Facebook button, the game suddently stopped linking with Google Play.
Whatever Sonic Dash version I was using, even the ones that worked before, the game asked me to update my Google Play services, so I did it.
Then I tried to link it again, and an error message appeared. I'm since unable to link the game with Google Play.
Even on my old phone, with old Sonic Dash version
Apparently, the last Sonic Dash version with Facebook function is 3.8.2.
The Facebook button is not present in version 3.8.3 and the following.
I guess you must keep an old version of Google Play to hope getting the "Friends Master" achievement.
But even with that, the Facebook button does not seem to work. I had old version of Facebook installed and that didn't change anything.
Any help will be very appreciated.