I just switched over to the new Gmail inbox with the smartlabel filters. Now whenever a social, promotions, updates or forums email comes in I get a notification on iOS from the Mailbox app. Previously I would just get notifications for "real" inbox emails. How can I continue to only receive iOS notifications for these?
As these emails are really in your inbox, you will receive notifications for them. My only suggestion is to use the gmail app in place of the ios mail app. The google gmail app allows you to specify for which folders you receive notifications for all new mail or 'primary only'.