AlwaysOn: Can reads on secondary block DDL on primary
Could someone explain, what the actual consequences are, if any?


Sure.


  On larger tables schema changes seem to cause a lot of blocking, which lead us to not applying some of our changes. 


This is happening on the primary (if it truly is blocking), you'll need to find what sessions are blocking it at why (on the primary for the primary).


  We got the advice to disable ReadOnly connections to the secondary replicas for the schema migrations.


This won't help the blocking, it could lessen it but only if the secondary is in synchronous commit mode and only if the workload on the secondary is causing extra HADR_SYNC_COMMIT waits. If it isn't, then it's not going to help the primary for blocking.

What turning off readable seconaries will do, is stop the workload on the secondary allowing it to have the most speed in keeping up by not having any other workloads to contend with. It may also help with redo blocking on the secondary since you're running DML and could lessen the send queue/redo queue. If you had synchronous replicas you may want to look at making them asynchronous for the time being depending on if the schema changes are size of data operations or not.


  From what I have read, I would guess that it doesn't, because reads at the secondary should not block dml queries on the primary.


Correct.