MantisBT currently supports Mysql and has support for other database engines.
The support for other databases is known to be problematic.
Having implemented the current database layer into Mantis 10 years ago, I'm currently working on replacing the current layer.
If you are interested in using Mantis with non-mysql databases - for example, Oracle, PGSQL or MSSQL, and would be willing to help out testing the new database layer, please drop me an email at email@example.com
In the meantime, I'd advise running Mantis with Mysql Only to avoid issues.