Culture, as I understand it, is not exactly something that can accepted or rejected, and I find it difficult to compartmentalize culture, politics, society, etc. I also tend to think of cultures (plural, or as you suggest subcultures) rather than monolithic culture.
That said, your question brings up notions of cultural hegemony, which is to say the use of culture as a means of domination. Likewise, there are numerous critiques of art as a bourgeois cultural replication mechanism. Culture, to some points of view and using here a more monolithic sense of the term, has historically been co-modified and, of late, has metastasized into a consumerist ethos where icons and brands dominate the cultural landscape. If this is what you mean by culture, then yes, I think it should be rejected, as with other forms of domination anarchism rejects.
I think an anarchist definition of culture would acknowledge that culture(s) is something everyone plays a part in creating, and not something to be simply consumed; culture not as big name stars and best sellers, but as an expression of liberation; in short, a peoples' culture rather than a culture of the elite. This definition brings with it bias, as I work in the cultural industry, and I acknowledge arguments which suggest an ideal anarchist society would have no need for the material trappings often associated with culture, such as novels, paintings, sculpture, etc., and perhaps no need of what is typically called culture at all...
There are a few other questions on Anarchy 101 that touch on elements of this topic. The question linked below has a number of articles/books/resources that might be of interest to you as well: