There is a Hadeeth says that three things cancel the prayer: the passage of a dog, ass, and woman? Aa'ishah, may Allaah be pleased with her, rejected this Hadeeth on the basis of what she saw from the Prophet, sallallaahu alayhi wa sallam. According to her, the Prophet prayed while she was in front of him laying on the bed. Does the passage of these three things has to be before the Sutra or beyond the sutra? In case a woman is praying, does the passage of another woman cancels the prayer or should it be that of a man? Since Aa'ishah rejected this Hadeeth based on what she saw, which is for her a more authentic narration, can we rejected a Hadeeth based on its contradiction to Qur'an or to even stronger Hadeeth? Let me use an example:
Can we reject the Hadeeth (who ever changes his religion, kill him) based on the Qur'aanic verse: (There is no compulsion in religion)?

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.

The scholars differed in opinion whether or not the passing of a woman, a black dog or a donkey in front of a praying person, invalidates his prayer. Some of them are of the view that these three things do not invalidate his prayer, and this is the view of the majority of the scholars as they interpreted the Hadeeth that is mentioned in this regard to mean that the passing of the mentioned-three decreases the reward of the prayer but does not invalidate it.

However, some Companions, among whom are Abu Hurayrah, Anas and Ibn 'Abbaas, and a group of righteous predecessors, like Al-Hassan Al-Basri, may Allaah be pleased with all of them, hold the opinion that the passing of these three things invalidate the prayer. Some others are of the view that it is only a black dog that invalidates the prayer and not the woman or the donkey; this is the view of 'Aa'ishah and the opinion of the Hanbali school.

As regards your question whether this applies to the passing of these things between the praying person and the Sutra or beyond the Sutra (an object of a hand span height placed in front of the praying person to prevent others from interrupting his prayer), the answer is that if these things pass between him and his Sutra or if they pass in front of him while he has no Sutra, his prayer becomes void.

However, if these things pass beyond the Sutra, then this does not invalidate his prayer, and this is what is meant by the Hadeeth.

The Prophet said: "When any of you stands for the prayer and there is a thing before him equal to the back of the saddle, then this covers him, but in case there is not before him a thing equal to the back of the saddle, his prayer would be cut off by the passing of an ass, a woman and a black dog…." [Muslim] Another Hadeeth reads: "….But something like the back of a saddle guards against that." [Muslim]

As regards the passing of a woman in front of a praying woman, then this does not invalidate her prayer even according to those who are of the view that the passing of a woman in front of a praying man invalidates his prayer.

Ibn Hazm who is of the view that if a woman passes in front of a praying man, she invalidates his prayer, said: "A woman passing in front of another praying woman does not invalidate her prayer." This narration is consolidated by another narration: "The passing of a woman in front of a praying man invalidates his prayer…"

With regard to your question whether or not we can reject a Prophetic Hadeeth, and whether or not it is possible to reject the Hadeeth "whoever changes his religion kill him", then we say that first there is no contradiction between the verse of the Quran and the Hadeeth. The meaning of the verse is that we should not compel a person to embrace Islam, this is crystal clear and no one should be forced to become a Muslim. Whomever, Allaah has guided to Islam, He has indeed guided his heart.

As regards whoever has embraced Islam and the truth had become clear to him and then apostates, he deserves death, because he rejected the truth after knowing it. So the meaning of the verse: {There is no compulsion in religion.}[Quran 2:256] is that there should not be any compulsion to enter Islam at the first place, but if someone enters Islam and then apostates, his just punishment is to be killed if he does not re-embrace Islam. However, it is only the ruler or his deputy that can execute such punishment or other kinds of punishments.

On another matter, it is only the scholars who could rule whether or not some Ahadeeth are contradictory, because they are more aware about whether or not some Ahadeeth are contradictory to others. The general public may think that there is a contradiction between one Hadeeth and another while in reality there is none. It could be that one Hadeeth is said in a general context and the second Hadeeth is in relation to a particular matter, or that one is absolute and the other is restricted, or that one is abrogating and the other is abrogated. Only the scholars know these matters and can distinguish which is which, contrary to other people who spend all their life playing and wasting time and then want to give Fataawa in the matters of religion and reject authentic Prophetic Ahadeeth that were reported from the Prophet .

Allaah Knows best.