Indeed, the issue of saying “amen” after the imam in Prayer or not saying it is subject to disagreement among Muslim jurists. All schools agree that saying it or missing it doesn’t affect the validity of one’s Prayer.
Dr. Sano Koutoub Moustapha, professor of fiqh and its principles, International Islamic University, Malaysia, states the following: “For Malikis, you should not say it at all. For Hanafis, you should say it but in secret, not loudly. As for Shafi`is and Hanbalis, you should say it loudly. Each of these opinions has its sources and evidences. However, all schools agree that saying it or missing it doesn’t affect your Prayer. Hence, it is considered as a recommended act according to the Shafi`is and Hanbalis, while the Malikis don’t recommend it.
Having said that, I can tell you that I do recommend saying it; thus there are a few hadiths in Muslim’s authentic book of Hadith and other Hadith collections which strongly recommend it, based on the practice of the Prophet (peace and blessings be upon him). Yet I call upon you and all beloved Muslims to tolerate and accept the different opinions in regard to this issue. This is due to the fact that the issue is considered as a matter of ijtihad and we need to forgive and tolerate one another in such issues.
The same thing, for example, applies to the issue of performing two rak`ahs when you enter the mosque on Friday and you find the imam delivering his sermon. For those who are willing to do so, they shouldn’t be prevented from doing. At the same time, those who are not willing to perform it should not be forced to do so.
Furthermore, how close to or far from the Sunnah a person is, should not be measured according to this single issue. In other words, we should not evaluate someone’s love of the Sunnah through this isolated action. Thus, nobody can claim that he or she can do all the Sunnah of the Prophet (peace and blessings be upon him). Therefore, we should not condemn or reject someone because of missing or not performing a sunnah, especially when that sunnah is subject to disagreement of the scholars”