You should be able to setup an ODBC connection to an .mdf file using the ODBC admin tool that comes with Windows. Tableau can then connect using the "Other Database (ODBC)" connection (last connection listed on the data connection screen).
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The MDF is one of (about) 3 files created by SQL Server. It sounds like VS may have installed SQL Server Express on your machine and is actively managing the MDF you see.
Use Tableau to connect to that local instance of SQL Server like you would any other SQL Server. You'll need the appropriate username and password, of course...