This app was mentioned in 10 comments, with an average of 4.50 upvotes
Okay there's a bunch of misinformation going on here.
This screen shows up when you activate an email account that uses the Exchange ActiveSync protocol. ActiveSync (AS) was designed to let corporate phones sync email/calendar/contacts/etc with a MS Exchange server. It also allows management of the device in question, including the ability to set a security policy (require a lock screen for example) and do a remote wipe.
Every single time you setup an Exchange ActiveSync account you will see this screen. Every time. There's not some power mad admin in your school's IT department who wants control over your phone, it's just a function of the protocol they use.
Now you have two choices.
Use a protocol other than Exchange ActiveSync. Ask your school to enable access via IMAP.
Use a different Exchange ActiveSync client, other than the one built into your phone. For example, TouchDown for Exchange is a 3rd party Exchange client with all the features (mail/calendar/contacts/etc). It will access your school's Exchange function, but with one big difference- a remote wipe only wipes the data in TouchDown, NOT the whole phone. I use TouchDown myself and I highly recommend it.
There's also Outlook for Android, but I've never used that so I can't comment with any authority.
Given your situation, I think you should give TouchDown or something like it a try.
I don't know about Nine, but most MDMs have integration with Touchdown. Policies are applied to the app in a containerized environment, meaning my corporate data through EAS is compliant, e.g. PIN security, but I can still change security settings on my phone, e.g. slide to unlock.
It's not the prettiest app but I've been using it for a few years and have grown used to it. I like having my EAS items completely separate from my personal stuff.
Check out TouchDown. The interface is straight out of Gingerbread, but it does a good job compartmentalizing exchange data and I can use it with a swipe-only lock screen with no security.
Touchdown is a similar app I've used for the same purpose in the past. Nine Mail seems to be more actively updated, and is also better polished IMO, but they both do the job. There are probably other options as well.
Not sure but this may work for you - Touchdown
Haven't used it myself but was curious and googled
I use Newton still, and am on the lookout for good alternatives. All the ones you mentioned I had tried over the last few months but none satisfied me so I finally bought Newton for a year
I actually prefer this client for stability and clearing up connectivity issues: https://play.google.com/store/apps/details?id=com.nitrodesk.droid20.nitroid
Try the trial, see if you get the same results.
Touchdown for Android
https://play.google.com/store/apps/details?id=com.nitrodesk.droid20.nitroid
Edit: added play store link