As it turns out, OEMs and carriers have taken matters into their own hands for video chatting. Some carriers, including Verizon, T-Mobile, and others have video calling built into every phone sold by the carrier. You can quickly and easily video chat with anyone else on the service. Thus, someone with a Galaxy S7 on T-Mobile and someone with an LG V20 on T-Mobile can video call each other directly from the dialer app like you were making a phone call. They're a bit restrictive, but they tend to work pretty well when you can actually use them. We hope these options are expanded over time.
Signal Private Messenger is one of the most popular privacy chat apps. It features end-to-end encryption for all messages, voice calls, and video chats between two Signal users. It focuses a lot on individual chats. There are group chat features, but it's mostly for personal use. This is one of the biggest differences between it and rival privacy chat app Telegram. Video calls worked fine in our testing so we have no trouble recommending them. It's a neat way to get some encrypted chats as well. The app is also completely free and open source. You can't really go wrong with it, but there are better video chat apps if you need group video chats.