How common are academic positions in theoretical physics offered to master graduates?
Masters graduates in physics are often offered paid positions as PhD students.  Otherwise it is very rare to obtain a full-time teaching or research job without holding a PhD.  Part time jobs, like adjunct instructor, may be possible.

Formerly it was possible to get a job at a less competitive institution like a community college or a university in a developing country.  However, while such jobs may still only require a Master's, in practice it is now easy enough to find a PhD holder to fill them.

You may be able to get funding which is intended for PhD students without completing a PhD.  But it is not clear why you would want to.