You can move either tensor to either side. It makes no difference to anything. Because we don't know what dark energy/the cosmological constant is you can argue that it's a part of spacetime or it's a part of the contents of spacetime, and then it kind of makes sense to put it with the Einstein tensor or with the stress-energy tensor just in a birds-of-a-feather kind of way. The maths is the same, whichever side you put it.
You can take the stress-energy tensor to the same side as the Einstein tensor if you like. It doesn't make matter into a vacuum (unless it was already a Hoover).
"Two apples equals two apples" is equivalent to "two apples minus two apples is no apples". Neither statement makes any difference to the contents of my fruit bowl.