However, this triggers a BOOST_STATIC_ASSERT in basic_xml_oarchive<Archive>::save_override<T>(const T&, BOOST_PFTO int).

The implementation insists that all serialized types be wrapped in a nvp<T>.

That is the intent.

But I couldn't find an explanation in the docs what special steps a user is supposed to take if the data shall be serialized into an xml archive. (The only hint that xml archives need special care that I found was the description of the header file nvp.hpp libs/serialization/doc/headers.html: "To associate a name tag with a serializable object. This is necessary to properly render an xml archive which includes the object name." BTW, this webpage claims nvp.hpp is in boost/archive, but in fact it is in boost/serialization.)

Do I need to write

ar & nvp<MyMemberType>("my_member_tag", this->my_member);

in my serialization functions for every variable I want to (de-)serialize? Can I choose an arbitrary tag for each variable or is it supposed to be consistent for all variables of a specific type?

Oh - no. Use the variable name for the tag not the name of the type. This is encouraged by usage of the idiom ar & BOOST_SERIALIZATION_NVP(my_variable);

Am I correct to assume that the code will still work if I serialize into a "normal" text archive and the nvp will essentially be ignored?

And all other archives as well - with no extra runtime overhead (assuming a decent optimizing compiler) There a section Reference:Class Serialization:Serialization Wrappers:Name-Value pairs where this is described. Perhaps this isn't obvious from contents.

May I suggest that a section explaining the issues with xml archives be added to the docs before the 1.32 release?

Yes you may.