Is it safe to move GPT formatted mdf file to MBR formatted disk?
In general SQL Server will not care that the database files are on a GPT or MBR formatted drive. You could use could use a floppy drive if you could find one big enough to hold the database (ouch on performance though! )

The only time it will be an issue is, as @James-Jenkins mentioned, if the size of your database files exceed the limits of what am MBR formatted drive can handle. This is 2TB. For a GPT drive it's 9.4ZB (9400 Terabytes!). Windows restricts this to 256TB.

If the MBR drive is running on a slow interface (USB1?) then you may experience IO performance issues but it shouldn't cause SQL Server to not run.

Investigate Windows system and application Logs in event Event Viewer to see if there are any messages related to the drive or the IO subsystem.

Check the disk using a testing tool to see if it's dying. If it's having problems you don't want to put your database on it.