All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
A Muslim should not follow the funeral procession or attend the funerals of a non-Muslim even if he is his colleague. On the contrary he is obliged to avoid all of this and let the followers of his religion (i.e. the non-Muslim) do the burial (and other related matters). This is the view of the majority of scholars. Ibn Taymiyyah, may Allaah have mercy on him, was asked whether or not it is permissible for Muslims who are neighbours of Christians to visit them when they are sick, or follow their funeral procession when they die; and if a Muslim who does is he sinful or not? He replied: "All perfect praise be to Allaah, it is forbidden for a Muslim to follow the funeral procession of a non-Muslim, but there is no harm for him to visit him when he is sick, as by doing so there is a benefit of softening his heart to accept Islam, because if he dies as a non-Muslim, he will go to Hellfire, it is for this reason that it is not permissible to pray the funeral prayer on him.'
However, some scholars are of the view that it is permissible to attend the funeral procession of non- Muslim relatives. Their evidence is the narration reported by Ibn Abu Shaybah that Abu Waa'il said: "My mother died and she was a Christian so I came to 'Umar and informed him about it, so he told me: "Ride a camel and precede the procession." But if the deceased is not a relative then it is not permissible to attend his funeral procession or attend his burial as some scholars stated that it is forbidden to attend a funeral procession of a non-Muslim. The above is all about attending the funeral of a non-Muslim, as regards attending the crematorium this is even worse as by attending the burning of the body one agrees to the falsehood that is happening as it is forbidden to burn the body of a dead person.
Allaah Knows best.