There is going to come a time when Christians will attend a funeral being conducted by denominational people. And because Christians see things as God would, one must be careful so that his actions don't give favor to the false doctrines and man-made rituals he will be subjected to. One thing we must remember is to comfort the living, for the person in the coffin is gone and there is nothing that can be said or done to help him or her (2 Samuel 12.23; Ecclesiastes 9.4-10). Some people hold special services to pray for the soul of the dead and certainly a Christian cannot partake in such.
We can render words of encouragement as well as a chance for the lost to learn truth by delivering the eulogy where the gospel can flow forth, and by mingling with the families afterward. There can still be opportunities to give warnings so people will be sure they are right with the Lord.
I remember standing graveside as a coffin was being lowered into the earth and a man saying "At least his problems are over." My reply was, "Not if he died in his sins". The man looked shocked—you could see that he had never read John 8.21. Yes opportunities can be found in the house of mourning so let us take full advantage of that fact (2 Timothy 4.2; 1 Peter 3.15).
As it has been pointed out when sitting in the audience of a denominational funeral, Christians must not participate in the falseness of the service. At many of these funerals, there will be singing with mechanical instruments and prayers uttered by false teachers with some of them being women. The Bible teaches not to have fellowship with unfruitful works of darkness; so that being the case, a believer couldn't go along with such nonsense because he knows better. The most that a Christian can do is not give the impression that you agree; for it is very likely the woman will be teaching something false, and also because it is wrong for a woman to teach and usurp authority over men (1 Timothy 2.12).
Now someone may say; "But wouldn't that make me appear to be rude?" Remember that Christians stand for truth first and people acceptance second (Acts 5.29; Luke 14.26). By sending a message of disapproval someone might ask you why you aren't participating, and you will have a chance to set up a study with that person (1 Peter 3.15).
Another thing I have seen at denominational funerals is the priest asking everyone in the audience to repeat the Apostle's Creed which was on printed material given to each person that came though the door. As I read it I noticed one of the lines to be repeated was, "I believe in the Catholic church." No way, was I going to utter this which was written by false teachers stating things in conflict with the Bible (Galatians 1.6-8). So I didn't do it. Some people saw me sitting in silence, and I was ready to make a stand for the truth but no one asked me anything.
I have seen churches ask for a moment of silence as they serve the Lord's supper at a funeral in the middle of the week; which is contary to God's word (Acts 20.7). I have seen people read farewell letters to the body in the coffin and the host asking everyone in the audience to say "Amen" to the reading. A Christian cannot do that either because the Bible teaches that the dead can't hear someone reading a letter to them back here on earth (Eccl. 9.4-10; Luke 16.26).
As a personal opinion, I'm considering avoiding denominational funerals. Maybe just attend the viewing because to go to these gatherings and be subject to some of that stuff is hard (Acts 17:16).
In closing, always remember that we must represent the truth 24 hours a day and no event that we attend will release us from our commitment to the truth. So let your light shine so those in darkness can know they are in darkness (Titus 2.1-15; 1 Peter 2.9). If people don't like your stand for truth that will be their problem to take up with the Lord, so let the dead bury the dead (Matt. 8.22).