The funeral prayer is a communal obligation (fard kifaayah) that must be offered for anyone who dies and was apparently Muslim, even if he or she committed major sins. 

An-Nawawi (may Allah have mercy on him) said: 

Offering the funeral prayer for the deceased is a communal obligation with no difference of opinion among us, which means there is (scholarly) consensus.

End quote. al-Majmoo‘, 5/167 

There is no shar‘i evidence to suggest that there was any exception to offering the funeral prayer for any Muslim except the shaheed (martyr) who was killed in battle. 

Ibn al-Qayyim (may Allah have mercy on him) said: 

The funeral prayer is not to be offered for the martyr who was killed in battle, because the Messenger of Allah (blessings and peace of Allah be upon him) did not offer the funeral prayer for the martyrs of Uhud, and it is not known that he offered the funeral prayer for any of those who were martyred fighting alongside him in his campaigns. The same is also true of his successors, the Rightly Guided Caliphs, and their governors and commanders.

End quote from Zaad al-Ma‘aad, 3/217 

See also the answer to question no. 14012 

With regard to the miscarried foetus, if it had not reached four months’ gestation, no funeral prayer is to be offered for it because it is not regarded as human and the soul had not yet been breathed into it. If it is miscarried after four months of pregnancy, then the funeral prayer is to be offered for it. 

The scholars of the Standing Committee for Issuing Fatwas said: 

If the foetus had not reached four months’ gestation, then it is not to be washed and the funeral prayer is not to be offered for it; it is not to be given a name and no ‘aqeeqah is to be offered for it, because the soul had not yet been breathed into it. 

End quote from Fataawa al-Lajnah ad-Daa’imah, 8/408 

There are some individuals whose situation is not clear to others, so people think that they are Muslims and offer the funeral prayer for them, when in fact they are not Muslims, such as apostates and hypocrites. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

The apostate of any type is not to be treated in the same manner as one who is originally a kaafir; rather he has to return to Islam. If he becomes Muslim again, all well and good; if he does not become Muslim then he is to be executed as a kaafir. He is not to be buried with the Muslims and the funeral prayer is not to be offered for him. 

End quote from Fataawa Noor ‘ala ad-Darb, 14/6 

With regard to the hypocrite, who is the one who conceals kufr whilst outwardly appearing to be Muslim, if it is known that a person is a hypocrite, then the funeral prayer is not to be offered for him. 

Allah, may He be exalted, says (interpretation of the meaning):

“And never (O Muhammad SAW) pray (funeral prayer) for any of them (hypocrites) who dies, nor stand at his grave. Certainly they disbelieved in Allah and His Messenger, and died while they were Fasiqoon (rebellious, - disobedient to Allah and His Messenger SAW)”

[at-Tawbah 9:84]. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:

If it is known that a person is a hypocrite, it is not permissible to offer the funeral prayer for him or pray for forgiveness for him. If no such thing is known about a person, then the funeral prayer should be offered for him. If an individual knows that a person was a hypocrite he should not offer the funeral prayer for him, but those who did not know that he was a hypocrite may offer the funeral prayer for him. 

‘Umar (may Allah be pleased with him) used not to offer the funeral prayer for one for whom Hudhayfah did not offer it, because during the campaign to Tabook, he knew who the hypocrites were who planned to kill the Messenger of Allah (blessings and peace of Allah be upon him). End quote from Minhaaj as-Sunnah, 5/160 

And Allah knows best.