The conversion from PostgreSQL to MS SQLServer isn't really a Tableau specific issue, so a more general search of the web might produce a solution. From what I can see, there are some tools available out there that can assist with the conversion/sync'ing of PostgreSQL to MS SQLServer. These tools should provide you with a way to automate moving the data from PostgreSQL to SQLServer on an automated schedule.
Now, if you are wanting to export results from Tableau (for example calculated fields) to SQL Server, then it becomes a more interesting process. You might be able to accomplish this by exporting the data from a data extract and then importing it into MS SQLServer, and this process might be able to be somewhat automated using tabcmd. But this ventures well into an area that I'm not as familiar with since things normally go from SQL Server to Tableau rather than the other way around.
Hope this helps
Did you ever find a solution for this? I am currently needing to do the same thing you requested above.
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You can achieve this by using your SQL Server. Use ETL tool (SSIS). Before you proceed for ETL development, you have to installed Postgres ODBC drive from below url
From here onward use Postgres Database as source and and destination will be your SQL server.
I did this for few of my customers in India, with same approach. If you need any of my help please let me know.
Sample Data Loading using Pentaho ETL tool--->