The answer is – it all depends. Canon law permits them to receive in the Catholic Church under certain, very precise, conditions (mostly life-and-death situations). However, the Orthodox Church does not permit its members to partake of communion in Churches that are not in communion with them.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.