In the case of Xoshiro256 you can just make multiple instances of the generator with Xoshiro's jump function. No locking required and no overlapping sequences.
You're wrong. Remember that XOR works on individual bits. If what you're saying was true, then swapping bits that are both set to 1 would also fail, which means this algorithm wouldn't work at all.
Edit: Ignore this post, I misread the original post as saying swapping the same values would fail.