Be careful when you’re asked to install a profile.
MDM Profiles allow remote administration, including options to modify settings, disable your ability to back up the device, as well as the remote wipe feature, which allows the administrator to erase all data from your phone (not just work stuff, but also personal things: photos, apps, messages, and basically everything else).
Besides, profiles can enforce your device to trust certain resources (websites, for example)—even if they’re not that secure and wouldn’t be trusted under normal circumstances.
MDM is a convenient way to manage devices that a company distributes among its employees. But I wouldn’t be comfortable with enabling my personal device for remote administration. All basic features—email (including Exchange accounts), calendars, and more—can be set up without MDM.