Thanks, all of you for the replies. But it seems that you are imagining a different kind of user than me. I don't think that there's anybody out there who could offer me better a perspective on the relative merits or applicability of the various models. My questions are strictly about whether or not I can use the Macbook and/or the Macbook Pro with hardwired Ethernet LANs (I've not been paying attention to the technical spec's of either laptop for years, and so don't know about the ways that can be used to "divide" high speed I/O channels like ThunderboltX, and others).
Also, this is not about making a choice between the Macbook and Macbook Pro. If both of them can do the video & LAN simultaneously, we will probably buy multiples of each. We don't need any advice about what either is appropriate for. They both have their uses here. And certainly, we don't need them to take the places of more high-end machines like the Mac Pro or other high performance Unix boxes. We're awash in such machines.
Elwe seems to be closest to my wavelength. Thanks Elwe for the dock idea. I hadn't thought of that. But I will in fact be using 4096 x 2160 resolution on the external displays, and will want to use Ethernet (and power) at the same time (with the displays). I don't prefer to use an adapter. A dock would be fine if it could do what we want. Your whole paragraph about the MBP is congruent with my thinking, and just the kind of reply that I was hoping for. Except no, the "configuring like to like" thing isn't of concern at all, and no, I don't have a video, song or photo collection to take into consideration, either. I will upgrade them to bigger storage anyway though, since we'll be using video all the time (we produce video). We loathe cloud storage, for whatever that's worth, and won't incorporate it into our model.
So if we can use Macbook Pros with (at least 1Gb) Ethernet, while simultaneously driving two 4096 x 2160 external displays, we will buy some of those. If we can use Macbooks with Ethernet while simultaneously driving one 4096 x 2160 display, we will buy some of those too.
Thanks again everyone, for taking the time to reply.