There are some things which might be indications of the sort of radically egalitarian ideals with which we tend to identify in contemporary culture. First, the Buddha did not seem to take seriously the claims of the Brahmins that they were superior and destroys their arguments to the contrary quite thoroughly within the intellectual framework of the time. Second, the Buddha did not set up a hierarchy among the monks of the Sangha. Third, the Buddha permitted the establishment of an order of nuns following his teachings, albeit somewhat reluctantly after some persuasion on the part of those who wished to follow his Eightfold Path.
Given these items, let's consider what feminism is and how coherent it would be with Buddhism. Our first look at feminism should start with a definition of it, specifically that feminism is a belief in the equality of the sexes and an advocacy for a recognizance of that equality in our human social structures. Obviously, there is significant disagreement between and among first, second, and third wave feminists regarding the precise meaning of equality and how the recognizance of it in human social structures should be implemented. Accordingly, we need to consider more specific claims regarding equality and human social structures to see if Buddhism might be compatible with those particular perspectives.
Some feminists reject the notion of women being obedient or submissive in the household, and the feminists who do so are probably not going to be able to reconcile their perspectives with the teachings of the Buddha. For example, let's consider an excerpt from one passage from a discourse of the Buddha on the woman of the home.
"Visakha, when a woman possesses four qualities she is heading for victory in the present world and is successful in this world. What four? Here, Visakha, a woman is capable at her work; she manages her domestic help; she behaves in a way that is agreeable to her husband; and she safeguards his earnings. ... And how does a woman behave in a way that is agreeable to her husband? Here, Visakha, a woman would not commit any misdeed that her husband would consider disagreeable, even at the cost of her life."
There are other passages which indicate that the Buddha viewed the role of the wife in the household as the more submissive and obedient role, but this particular passage is quite stark and makes it very clear that certain forms of feminism are not compatible with Buddhism.
This of course begs the question: what forms of feminism might be compatible with Buddhism?
It's certainly possible that feminists who are simply advocating equal rights under the law (e.g. voting rights) could have a perspective compatible with the teachings of the Buddha. The Buddha did not advocate for changes to the political structures of the day, probably because he was more interested in helping people get to the other shore, as I've mentioned previously. What he did advocate was behavior on the part of political leaders that was in agreement with the eternal moral law. Specifically, the ideal ruler extended his protection to all as we see in the below passage.
"In this case, the wheel-turning monarch, the just and righteous king, relying on the Dhamma, esteeming and respecting it, with the Dhamma as his standard, banner, and sovereign, provides lawful protection, shelter, and safety for his own dependents. He provides lawful protection, shelter, and safety for the khattiyas attending on him; for his army, for the Brahmins and householders, for the inhabitants of town and countryside, for ascetics and brahmins, for the beasts and birds."
There are certainly hints here of a certain kind of equality under the law, albeit within a distinctly patriarchal framework. Ultimately, it is possible to reconcile certain kinds of feminist ideals with Buddhism, but not possible to reconcile other feminist ideals with the Buddha's teachings. The answer to the question of whether feminism is compatible with Buddhism very much depends on what sort of feminism one agrees with.