You are free to go to the services of other Christian denominations. We all have a duty to work together ecumenically to understand and respect each other with an aim towards eventual Christian union. Going to other Christian services is not only permitted, it is a very good thing to do.
Pray, sing and worship with our Lutheran brothers and sisters in Christ, but don’t take Communion.
DIRECTORY FOR THE APPLICATION OF PRINCIPLES AND NORMS ON ECUMENISM
vatican.va/roman_curia/po…ectory_en.html
Sharing in Non-Sacramental Liturgical Worship
116. By liturgical worship is meant worship carried out according to books, prescriptions and customs of a Church or ecclesial Community, presided over by a minister or delegate of that Church or Community. This liturgical worship may be of a non-sacramental kind, or may be the celebration of one or more of the Christian sacraments. The concern here is non-sacramental worship.
- In some situations, the official prayer of a Church may be preferred to ecumenical services specially prepared for the occasion. Participation in such celebrations as Morning or Evening Prayer, special vigils, etc., will enable people of different liturgical traditions—Catholic, Eastern, Anglican and Protestant—to understand each other’s community prayer better and to share more deeply in traditions which often have developed from common roots.
- In liturgical celebrations taking place in other Churches and ecclesial Communities, Catholics are encouraged to take part in the psalms, responses, hymns and common actions of the Church in which they are guests. If invited by their hosts, they may read a lesson or preach.