Feminism is not a single idea which can be accepted or rejected in one go. Rather, it is a collection of ideas which have evolved and are continuing to evolve. There are also different types of feminism.

So, it is better to evaluate ideas individually and decide whether or not they are acceptable or relevant, and then take what is good or useful and leave the rest. 

Not all Muslims will agree about individual ideas since they have differing understandings of Islamic scripture, human nature, social ideals, the authenticity of certain hadith, conceptions of Islamic law, and the will of God, but at least an attempt can be made.

The same is true for almost any -ism. 

Much of the opposition to feminism has been rooted in politics, especially resistance to colonialism/post-colonialism, as it has been felt that the West used feminism/women's rights as a tool to try to dominate Muslim societies. When one looks at the mass media from certain countries, for instance, women's issues being used as a pretext to glorify invading a Muslim country, one can see there is still some truth to this. 

However, the response by Muslims has often been to celebrate or impose restrictions on women, in the name of fighting the West and preserving Islam. This doesn't benefit Muslims in the slightest.

Furthermore, one often hears "equality between men and women is a Western idea which they are trying to impose on us; therefore, we must fight against the equality of women." This, similarly, is unhelpful, since it is a statement made in a politicized context, and shuts down a possibility of a nuanced, de-politicized discussion about important social issues. One cannot develop when in a defensive posture.

There is no question that basic issues surrounding women's rights have been serious concerns in some modern Muslim-majority countries and communities, and indigenous activism by Muslim women has been crucial to fixing social wrongs. 

Today, discussions about the situation of women or attempts to fix problems, or to root out wrong ways of thinking, are sometimes shut down by calling people "feminists" as a derogatory term. (That is, the discussion is shut down by name-calling, rather than actually addressing the issues at hand.) This, too, helps no one.

So it is good to consider the underlying dynamics behind how feminism is discussed since the ideas themselves are not wholly politically neutral. 

The other main concern about feminism has been that much of it reflected a middle-class white Western European/American experience, and some ideas were exported which were not relevant globally or to all people, although there are other types of feminism that have developed in response to this. So, relevancy can also be considered when considering the merit or demerit of ideas. If an idea isn't relevant, it can also be discarded.