MySQL is almost a de facto standard for web development, and most
people are so ignorant that they think MySQL is the only RDBMS that
plays nicely with any platform. Obviously, it may be the most widely
used RDBMS in web apps, therefore, you will find much more volunteers
to add support for it. But, as far as I know Postgres plays nicely
with Rails. I haven't tried it myself, but I have had people report
that it does work nice with it.
It is true that Rails does not work nicely with a few RDBMSs, but that
has to do with the fact that the majority work with MySQL, hence you
will tend to get more support for MySQL.
If you don't want to lose the contract, then just do what they say: go
with MySQL. The only problem that I see with MySQL is the licensing
scheme, which isn't very attractive.