Proposed resolution (August, 2017):

Change 13.9.3 [temp.explicit] paragraph 1 as follows:

A class, function, variable, or member template specialization can be explicitly instantiated from its template. A member function, member class or static data member of a class template can be explicitly instantiated from the member definition associated with its class template. An explicit instantiation of a function template or, member function of a class template, or variable template shall not use the inline or constexpr specifiers.

[Accepted as a DR at the November, 2017 meeting.]

According to 13.9.3 [temp.explicit] paragraph 1,

An explicit instantiation of a function template or member function of a class template shall not use the inline or constexpr specifiers.

Should this apply to explicit specializations of variable templates as well?

(See also issues 1704 and 1728).