Nothing stopping you using another database - I've started using CouchDB with an ASP.Net MVC application and it all hangs together pretty well.
You could use MySQL, PostgreSQL, SQLite etc. just as easily.
You could use MySQL, PostgreSQL, SQLite etc. just as easily.
People are used to throw such examples in the air, like you forgot "hey, there's Mono if you want Linux" ... but how many real apps used by actual people diverge from the MS stack?
Hint: it's not ignorance.
I've designed ASP.Net apps that have had back ends of various forms (everything from navigational databases to Oracle OLAP systems) and once you get over the need to have direct support in Visual Studio then it's not really that big a deal.
YMMV.
A couple of complex queries not optimized at all where slow in MySql and very fast in SQL Server but I think that that is because of the database engine itself and not because of the driver.