Sorry, this is entirely a limitation of Microsoft Access.
You can use any other database, or text or Excel files, and you won't have this problem.
I've used Access *a lot* with Tableau and Dan's right, the limitations are all about MS Access. It's fundamentally built as a database for workgroups or small departments and doesn't have the capabilities that we might want. We can't have more than 255 columns in a table nor more than 255 columns in a query in Access. Also Access has some other size limitations (# of queries & tables, number of records, total size of data, complexity of query) and is much more sensitive to the quality of the network connection than other RDBMS's I've used. In my case for Access data sources I almost entirely use Tableau data extracts because I find they are up to 100x faster than live connections.
I've been (slowly) moving our Access DBs onto SQL Server (both Express and a full install) and even with the added work I am much happier. There are no limitations on # of columns, much improved performance so live connections are more feasible, a lot more SQL features, views, stored procedures, improved security (which makes my IT department very happy), profiling, the list goes on and on.