This app was mentioned in 4 comments, with an average of 2.50 upvotes
It's just IMAP, CalDAV and CardDAV.
https://play.google.com/store/apps/details?id=org.dmfs.caldav.icloud
Notes are also just technically a folder in IMAP.
I have Reminders, Contacts, Calendars, Email all running on my Moto X. Photos don't naturally but you can use IFTTT to sync Android to iOS Photos.
I haven't used an iPhone for awhile but I otherwise live in the iCloud world. I sync Calendar & Contacts with these perfect apps. You just need to create an app-specific password.
https://play.google.com/store/apps/details?id=org.dmfs.caldav.icloud
Or this https://play.google.com/store/apps/details?id=com.smoothsync.icloud
This is really old & not updated for awhile but it still works for me: https://play.google.com/store/apps/details?id=org.dmfs.caldav.icloud