Raven now connects itself to the got_request_exception() signal to catch unhandled exceptions, bypassing the logging system entirely, so the solution proposed by dlowe does not work anymore.
However raven looks for a skip_sentry attribute on the exception instance, so you can use a middleware to set it on the errors you want to ignore:
import sys
import traceback
class FilterPostErrorsMiddleware(object):
    """
    A middleware that prevents unreadable POST errors to reach Sentry.
    """
    def process_exception(self, request, exception):
        if isinstance(exception, IOError):
            tb = sys.exc_info()[2]
            for _, _, function, _ in traceback.extract_tb(tb):
                if function == '_get_raw_post_data':
                    exception.skip_sentry = True
                    break
Note: you have to use a recent version of raven (e.g. 1.8.4), as previous versions mistakenly checked for the skip_sentry attribute on the exception type rather than instance.