1) If it's an SMS, which has no encryption possible
2) If it's going through the iMessage service, in which case it has all the protections and features that Apple puts there.
(At some point in the future, there will be a third way: if it's an RCS message. We don't fully know what features that will support on Messages, or what bubble color it will have.)
What you're suggesting would only make sense if there were some kind of "Messages API" that various companies could use to get their chat apps to interoperate with it. Maybe there should be, but there isn't, and suggesting, in isolation, that Apple separate out the security indicator from the platform indicator of the bubbles is like suggesting that supermarkets be required to put clear notifications on their apple pies that contain salmon.
That the conversation has turned into comparison to "contains salmon" labels on pies is a great example the strategy is wonderful at complicating any discussion around whether it should be opened up.