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I have just removed a bunch of wallpaper. It came off easily, but left paste residue behind.
My problem is that the wallpaper was put on over texture (no I did not do this; someone in 1978 did it.) and if I get it wet enough to get the dried paste off, the texture comes off too, making an incredible mess with gobs of goo.

Is there a way to get the paste off without also wetting the water-based texturing stuff? This was expected to be straightforward (ha ha) and of course is not since I am at a dead halt.

Hard to say exactly since you don't have any idea what is really on the wall. It's not easy to put wallpaper on over a textured wall finish. The most common way is to install a heavy 'mat' first to cover the texture. The 'mat' that I've used resembles a thick paper (maybe .030" thick or more) that is sort of 'spongy' and holds lots of paste.

You might be stuck with removing the texture, too. Otherwise... sanding might be the only other answer.

Are you planning to paint? ... or put on new paper?

Paint. But I do not hate the texture that is on there (called knock off or something like that) and the way it is going it would have to be re-textured, which I am not competent at.

I have a couple of areas in my house that I refer to as 'lazy plaster'... topping compound smeared on with a trowel to resemble stucco. It's a great way to hide ugly stuff with less ugly stuff!