Hello @zakonuzemunu,
As you discovered, PXC in strict mode does not allow DML to run on tables without primary key. This is done for several reasons, the main one being less data to synchronize between nodes when replicating and another big reason is for handling conflicts when writing to multiple nodes at the same time.
You can relax this requirement by setting pxc_strict_mode=PERMISSIVE or DISABLED.
The proper solution is to simply add a PK to the tables. Something as simple as id int unsigned AUTO_INCREMENT will be just fine. Your application won’t use it, so it shouldn’t impact the app.
Also, 2 servers with PXC is not advised. You should always have an odd number of nodes. If one of your 2 goes down due to crash/power loss/network outage, then both nodes will be down since only 50% will remain. You must have > 50% to be online.