This depends on the configuration of the MDM and the MDM vendor. For example, most MDM deployments to Android for instance conform to Android For Work, which functions in practice to a virtual machine from a user's perspective, and doesn't have access to a non workspace content. iOS has a similar functionality which, while less commonly used, is there specifically for use on personal devices to sandbox off 'work' content where pervasive features like factory resets and access to phone logs and sms records don't function, and you can't access the more advanced features without having purchased the device via a corporate account.

SimpleMDM has a credit card-less trial which you could set up to see what features exist and how they work from the vendor side. You won't have access to some of the 'supervised' features without being a business,but you can see the buttons offered when you aren't a corporate-purchased device readily enough.

For corporate owned devices, the rules are very different though.

I have a little experience with Microsoft’s intune and there are different ways to register devices. Someone feel free to correct me because I don’t feel like logging in to double check. Company owned devices have more control and can restrict apps, lock, full wipe, etc. Personal or “bring your own” devices are much less restricted. I can’t lock, wipe, or restrict apps. For the personal devices, it’s more about giving secure access to the companies resources and not really controlling the device. I work for a small business and only use this to setup access to non important documents for employees in the field so I know just enough to be dangerous.

I can’t read your emails, text messages, I can’t remote into your phone without your permission. The info we have is very limited. You know how we can see that information? If you gave us your phone and password :-)

I’m not sure what MDM you’re subjected to but I’ve been an MDM engineer for 7 years using Intune and JAMF and no, no SMS or phone records. Even the phone # is blanked out minus the last 4 digits. Yes we can wipe the devices if it’s lost\compromised but personal versus corporate owned devices are limited. I can’t see what apps you have that were personally installed. And the only info I can get are the device stats (SN, IMEI, storage, battery, memory, etc).

Can you support your claims? I’ve worked with Intune, Jamf, MaaS360, Citrix, and Workspace ONE and none of them could read texts, emails or browser history.

I’d be very interested to learn more about how they can access this information through MDM. We always did it through either the mobile carrier or the admin console for whatever the office/mail suite that was deployed.

Please cite any one of your sources. I've managed MDM for over a decade and you're spreading misinformation.

Absolutely none of the MDM products on the market allow for the reading of personal e-mail, SMS, phone records, etc. On the contrary, almost every single one provides an information screen during the enrollment that makes it abundantly clear that they do not (and can not) access that data. Moreover, the "wipe" of data is the removal of company data. It doesn't wipe your phone, it just removes the work profile (Android) or deprovisions the work profile and associated apps (Apple). All of your non-work-related data is untouched.

Quick Sources for Intune and JAMF -- do your own googling for others:
https://learn.microsoft.com/en-us/mem/intune/protect/privacy-data-collect
https://www.jamf.com/blog/apple-mobile-device-management-faq/