Can I store an array of class instances in Redux?

To quote redux docs (ref):

If you are okay with things like persistence and time-travel debugging potentially not working as intended, then you are totally welcome to put non-serializable items into your Redux store. Ultimately, it's your application, and how you implement it is up to you. As with many other things about Redux, just be sure you understand what tradeoffs are involved.

That said, when you use classes as value objects (which means they are immutable) and with no inheritance, it doesn't go against the spirit of react and it seems fine.

However, it's not clear from the docs what "can break the ability to persist and rehydrate the contents of a store" means. For example, when you store instance of such class with reducer and then retrieve it with selector, is it transformed (I mean serialized and deserialized) somehow on the way? If not, then it's fine as it's usable. If yes, serialize/deserializer wouldn't know how to (de)serialize it as JS doesn't have any general Serializable interface to implement which serializer could follow. In such way, using classes wouldn't be usable.

The plain JS values are simply a Plain Old JavaScript Objects (POJO):

var obj = {};// this is a POJO
var obj = new Object();// this is POJO

What is not a PJOJ, is something like this:

var Obj = function(welcome_text) {
  this.welcome_text = welcome_text;
}
var c = new Obj("Welllllcome!!!!");// this is not a POJO !

I folowed up the docs of redux, and they gived an example in this link. They explain that, for example, you can not have new Date() as a params for your actions/states, beacause the new Date() will return a non POJO ! Instead, you should do new Date().toISOString() wich will return a string.

So, to respond to your direct question (Can I add to redux an array of Conversation instances?)

YES YOU CAN.