Modifying a global variable in a constexpr function in C++17

Which compiler is correct?

Clang is right.

The definition of a constexpr function as per dcl.constexpr/3

The definition of a constexpr function shall satisfy the following
requirements:

(3.1) its return type shall be a literal type;
(3.2) each of its parameter types shall be a literal type;
(3.3) its function-body shall be = delete, = default, or a compound-statement
that does not contain:

(3.3.1) an asm-definition,
(3.3.2) a goto statement,
(3.3.3) an identifier label,
(3.3.4) a try-block, or
(3.3.5) a definition of a variable of non-literal type or of static or
thread storage duration or for which no initialization is performed.

Also as per dcl.constexpr/5:

For a constexpr function or constexpr constructor that is neither
defaulted nor a template, if no argument values exist such that an
invocation of the function or constructor could be an evaluated
subexpression of a core constant expression,

Foo(true) could be evaluated to a core constant expression (i.e 1).

Also, Foo(false) could be but is not required to be constant evaluated.

CONCLUSION

Thus, a bug in GCC.

Many thanks to @Barry, @aschepler and @BenVoigt for helping me with this answer.