I’ll try to give a *helpful* response.
The Xs (and Max) like the X, 8+ and 7+ before it, uses the dual lenses and parallax to determine what is in the foreground and what is in the background, much the same way your eyes and brain do. With only one lens, the Xr will do this using the autofocus phase detection pixels in the sensor to determine depth. Same idea but done computationally rather than physically (well, it is physical but at a much smaller scale, so it is enhanced computationally). Google does this with the single lens Pixel phones.
My understanding from the keynote is that you will still be able to use depth effects, like portrait mode. It just may not be at the same quality level as using a dual lens setup. I’m sure it will still be quite good, and I’m going to venture a guess that most people will not notice the difference. Too soon to tell for sure, though.
I don't think you can assume the "quality" of the XR's portrait mode will be any worse, because from what I've seen, the quality of the XS' and XS Max's portrait mode is still not great. There are still a lot of problem with portrait mode's inability to accurately find edges and blurring out foreground features of the portrait's subject. This is a problem that occurred with the introduction of portrait mode on the 7 Plus, and which still exists in the 2018 models. Maybe it's a bit better in the newer models, but it's still a huge problem. However, that relates to the computational aspect of the portrait mode.
The other aspect that many people don't talk about is the choice of lens used. By default, portrait mode on the flagship dual-lens phones utilizes the 2X telephoto lens. Likely one main reason this is done is because closeups with telephoto lenses look better to humans than closeups with wide angle lenses. Wide angle lenses distort the subject up close, so that noses are too big, etc. The technical quality of the image may be fine, but the image perspective is different.
I don't know how significant this will be on the XR, but I suspect it will be noticeable if you try to take too close of a portrait. I note from Apple's marketing materials that while they have very close closeups for portrait mode for the XS/Max, they don't for the XR, probably specifically for this reason.
That said, for my kids one of the annoyances I had with portrait mode was the forced utilization of the telephoto lens. Sometimes I just wanted a wider angle portrait for full body shots, etc.
