Implementing HA for SQL Server for a .NET Application that uses MS DTC
Here is the most complete official-ish statement available about the risks and consequences of using DTC in an unsupported configuration with AGs:


  This means you could test a cross database transaction, force failover
  and everything work fine.   Test again it fails.   It could
  be as simple as the controlling DBID changes on the secondary and the
  outcome of the cross-database transaction can’t be properly
  determined.
  
  For Availability Groups you should avoid the use of DTC and
  cross-database transactions.  Relying or using them could manifest as
  a problem with the database recovery activities and that is certainly
  not what you want in a HADR environment.


https://blogs.msdn.microsoft.com/alwaysonpro/2014/01/06/not-supported-ags-with-dtccross-database-transactions/

Note that all use of DTC with AGs was unsupported in SQL 2014 and before.  In SQL 2016 support was added for DTC transactions not involving multiple databases on the same instance.  In SQL 2017 that restriction was removed.