The Directory Concerning Ecumenical Matters: Part One explains when a Catholic may receive the Eucharist in an Eastern Orthodox church. Catholics may receive Communion there when “special circumstances make it materially or morally impossible over a long period for one of the faithful to receive the sacraments in his own Church, so that in effect he would be deprived without legitimate reason of the spiritual fruit of the sacraments.”
This provision doesn’t apply to those who have normal recourse to the sacraments in the Catholic Church.
The same document also emphasizes that attendance at Orthodox liturgies by Catholics is permitted “if they have reasonable grounds, e.g. arising out of a public office or function, blood relationships, friendships, desire to be better informed, etc. In such cases there in nothing against their taking part in the common responses, hymns, and actions of the Church in which they are guests.”