I am working with a client who is syncing between SQL Server and MySQL containing the exact same schema and data. We want to centralize that data into one database. Other
on the otherhand I think you've already mentioned what possible problems you may encounter when synchronizing 2 db at the same time aside from this two I think it would be the resources. since there are different RDBMS working for the application they would also have a separate resources for each, like when I update a particular record of a user it still needs to check on which resource does it really exist, but I love to hear more from other people out there this is really an interesting topic to discuss. ;)
You can create a linked server instance in SQL Server, with the MySQL instance.
Despite being completely proprietary, one of the nice connectivity features offered in SQL Server is the ability to query other servers through a Linked Server. Essentially, a linked server is a method of directly querying another RDBMS; this often happens through the use of an ODBC driver installed on the server.
Refer This article : step-by-step process SQL Server Linked Server to MySQL.
Providing you grant the MySQL user you connect on behalf of proper permissions, you can write to the MySQL instance accouding to you. So you can update stored procedures to do an additional step to insert records into MySQL.
Much easier solution is to use commercial application - Omega Sync from Spectral Core Omega Sync can compare and synchronize both database schema and table data. You can even synchronize data of heterogeneous databases (for example, compare your local SQL Server database with a MySQL replica on your web site - and synchronize all the differences in just a few minutes).