My children and I are progressing through RCIA. We are attending a non-Catholic funeral today and want to know the proper behavior to represent our new faith – while being respectful to the faith of the family. Do we bless ourselves? Do we bow before the altar? Any help would be a blessing.
Unless the funeral is being held in a church with a valid Eucharist (e.g., Eastern Orthodox), there is no need to genuflect or bow to the altar. Those gestures are intended to show respect for the Real Presence of Christ in the Eucharist, something that Protestant churches do not have. As for crossing yourself, that is up to you. If you ordinarily do so in prayer, it would not be wrong to do so at a non-Catholic Christian funeral. (Do not do so, at least not visibly, at a Jewish funeral though, as such a gesture may cause offense and scandal.)
As for dealing with the family, a general rule of thumb for showing respect is to show up on time, sit quietly, stand when the congregation stands, to greet the family and to offer condolences after the service. It is also nice to sign the guestbook, if one is available, and to write a personal letter expressing condolences and perhaps sharing special memories of the deceased. For more information on how to attend the funeral of someone of another religion, see the book linked below.
How to Be a Perfect Stranger by Stuart M. Matlins and Arthur J. Magida