Can a bool read/write operation be not atomic on x86?
It all depends on what you actually mean by the word "atomic".
Do you mean "the final value will be updated in one go" (yes, on x86 that's definitely guaranteed for a byte value - and any correctly aligned value up to 64 bits at least), or "if I set this to true (or false), no other thread will read a different value after I've set it" (that's not quite such a certainty - you need a "lock" prefix to guarantee that).
x86 only guarantees word-aligned reads and writes of word size. It does not guarantee any other operations, unless explicitly atomic. Plus, of course, you have to convince your compiler to actually issue the relevant reads and writes in the first place.
There are three separate issues that "atomic" types in C++11 address:
tearing: a read or write involves multiple bus cycles, and a thread switch occurs in the middle of the operation; this can produce incorrect values.
cache coherence: a write from one thread updates its processor's cache, but does not update global memory; a read from a different thread reads global memory, and doesn't see the updated value in the other processor's cache.
compiler optimization: the compiler shuffles the order of reads and writes under the assumption that the values are not accessed from another thread, resulting in chaos.
Using std::atomic<bool> ensures that all three of these issues are managed correctly. Not using std::atomic<bool> leaves you guessing, with, at best, non-portable code.