The new version 0.8.1 of the WebIssues Server supports both MySQL and PostgreSQL databases. Now it should be possible to install it in most hosting environments. If you have any problems with the installation, please contact me.
Another important feature of the 0.8.1 version is that the schema version is now stored in the database, which makes it easier to update the database in the future. For now the schema was changed so much that an automatic update would be too difficult, but I think it should be more or less close to the final state now.