Forsaking Your Muslim Brother because of Differences in Opinion
Question

I know that it is only permissible for a Muslim to be mad at a fellow brother for 3 days at most, and the one who is better is he who talks first. However, if I only see a certain brother once a week or so, is it permissible for me to turn away 3 times that I see him، or do I have to stick with the 3 day limit. If I do,  then he will never know my displeasure with him. I know this isn't a good attitude to have, but sometimes a brother may do something and I would like to let him know that I do not approve of it.
Praise be to Allah.It is not permissible to forsake a Muslim, because the Prophet (peace and blessings of Allah be upon him) said: “It is not permissible for a man to forsake his Muslim brother for more than three days, each of them turning away from the other when they meet. The better of them is the one who gives the greeting of Salam first.” (Narrated by Al-Bukhari, 5727; Muslim, 2560)
If the believer is a relative, such as a brother, nephew, uncle or cousin, then forsaking is an even worse sin. 
This applies unless the person is committing a sin and there is an interest to be served by forsaking him, i.e., it will make him give up the sin. In that case, there is nothing wrong with it because this comes under the heading of removing evil. The Prophet (peace and blessings of Allah be upon him) said: “Whoever among you sees an evil action, let him change it with his hand [by taking action]; if he cannot, then with his tongue [by speaking out]; if he cannot then with his heart [by hating it and feeling that it is wrong], and that is the weakest level of faith.” (Narrated by Muslim, 49)  
The basic principle is that it is prohibited for a Muslim to forsake his fellow-Muslim unless there is a reason to allow it. (See Fatawa Manar Al-Islam, by Ibn ‘Uthaymin, vol. 3, p. 732) 
Wali Al-Din Al-‘Iraqi said: 
“This prohibition applies in cases where the forsaking is caused by anger with regard to something permissible and has nothing to do with religion. With regard to forsaking someone for a religious reason, such as his committing sin or Bid`ah; this is not prohibited. The Prophet (peace and blessings of Allah be upon him) commanded (his companions) to forsake Ka`b ibn Malik, Hilal ibn Umayyah and Mararah ibn Al-Rabi’ (may Allah be pleased with them). Ibn ‘Abd Al-Barr said: This Hadith of Ka`b indicates that it is permissible for a man to forsake his Muslim brother if he commits some act of Bid’ah or immorality, in the hope that forsaking him may discipline him and serve as a rebuke to him. Abu Al-‘Abbas Al-Qurtubi said: With regard to forsaking a person because of sin or Bid`ah, it should be continued until he repents from that and does not go back to it. Ibn ‘Abd al-Barr also said: The scholars are unanimously agreed that it is impermissible for a Muslim to forsake his fellow-Muslim for more than three days, unless there is the fear that speaking to him and keeping in touch with him will affect one’s religious commitment or have some harmful effect on one's spiritual and worldly interests. If that is the case, it is permissible to avoid him, because peaceful avoidance is better than harmful mixing." (Tarh Al-Tathrib, 8/99)
What you should do, if your brother has done something prohibited, is to advise him and explain that this thing is prohibited, and remind him of Allah. If you see that he is persisting in his sin and you think that forsaking him will serve a purpose, then it is permissible to do so, as stated above. But if he has simply done something that you do not agree with, or it is the matter of different points of view, then you should explain to him that you do not agree with what he has done, or with his mistaken point of view. But if you make forsaking him the sign of your disagreeing with him, this may lead to him rejecting your view completely, let alone the fact that this is not a legitimate Islamic justification for forsaking him for more than three days. We have seen above in the Fatwa of Shaykh Ibn ‘Uthaymin that the basic principle is that it is prohibited for a Muslim to forsake his fellow-Muslim, unless there is a reason to allow it. 
The Muslim must be forbearing and sincere towards his brothers, he must be tolerant towards them and overlook their mistakes. He should not hasten to adopt a solution that may cause division and prohibited kinds of forsaking. May Allah help us all to do that which He loves and which pleases Him. 
For more details, please see the following answers: 13731 , 11018 , 126918 , 93775 , and 93146 .