Christian
Funerals are traditional and formalized, no matter how casual North American culture has become.
The Christian tradition of dressing in all black has largely been replaced by dressing in a somber colors, though black is always acceptable.
No revealing clothing, including sundresses or spaghetti straps. Don't wear your sexy leather pants or a mini skirt. No sandals.
Men should at minimum wear a jacket, trousers and dress shoes. Ties are preferred, but optional.
Best comment to the bereaved: I am so sorry. Say nothing else.
Buddhist
No display of wealth in jewelry or dress. Wear plain clothing of somber colors. The family of the deceased might wear white. Remain quiet and respectful. Women may wear long skirts, loose slacks and modest shirts with long sleeves. Men may wear somber-colored jackets and long pants. Dress may be somewhat casual. The service ranges from 45 to 75 minutes. You might want to follow the service by kneeling, so be sure your clothing allows it. Do not say the deceased is in a better place. You can say to the family: We are thinking of you.
Islamic
Non-Muslim men should dress nicely with a shirt, tie and dark jacket. Women should wear long skirts to at least the ankle with a long-sleeved shirt with neck covered. A head scarf is required. Wear socks, since you will have to take off your shoes if rites are held inside. But rites might be outside.
Do not talk at all. Do not take pictures at any time. Do not bring food to a funeral reception. Do not cry loudly or make any emotional sounds. Do not send flowers.
During the very short service, men and women line up separately for silent prayers: Men, then children, then women.
Hindu
Rites may be held in the home. Conservative dress for men and women is expected, but do not wear black. White or light-colored attire is appropriate. Sit quietly during the chanting at the funeral if you don't know the chants.
Jewish
Somber dress. Women should wear long skirts or dresses and have their arms covered.
Men should wear a dress shirt, jacket, and tie. No jeans. Never under-dress for a funeral. Don't send flowers. Casket will be closed. Services will be brief and may only be held at grave side.
Non-Jewish men may be asked to wear a yarmulke and women may be asked to cover their heads with scarves. Do not arrive late.