I was able to get it to work doing the following below. I'm running VS2012.2, MVC4 targeting .Net Framework 4.0. I deployed it to my .Net 4 server at my hosting provider (DiscountASP.Net).
Do NOT add MySQL.Data, MySQL.Data.Entities and MySQL.Web via NuGet. Instead download the .Net Connectors from the MySQL site. At the time of this post it was Version 6.6.5 for MySQL.Data, MySql.Data.Entity and MySql.Web. If you already do have them from NuGet be sure to un-install them from the package manager.
Manually add the MySQL asm refs for .net 4 to the project from where MySQL installs its .net Connectors (mine was in C:\Program Files (x86)\MySQL\MySQL Connector Net 6.6.5\Assemblies\v4.0). Be sure to check Copy Local for all three of the asms.
Add or modify the following in your web.config:
In the <configuration><connectionStrings> section:
<add name="MyProviderDbConn" connectionString="server=mysql01.someurl.com;User Id=dbuser1;Pwd=ToManySecrets;Persist Security Info=True;database=MyDbSchemaName;Use Compression=True;port=3306" providerName="MySqlMembershipProvider" />
In the <configuration><system.web> section:
<membership defaultProvider="MySqlMembershipProvider">
<providers>
<clear />
<add name="MySqlMembershipProvider" type="MySql.Web.Security.MySQLMembershipProvider, MySql.Web, Version=6.6.5.0, PublicKeyToken=c5687fc88969c44d" autogenerateschema="true" connectionStringName="MyProviderDbConn" enablePasswordRetrieval="false" enablePasswordReset="true" requiresQuestionAndAnswer="false" requiresUniqueEmail="false" passwordFormat="Hashed" maxInvalidPasswordAttempts="5" minRequiredPasswordLength="6" minRequiredNonalphanumericCharacters="0" passwordAttemptWindow="10" passwordStrengthRegularExpression="" applicationName="/" />
</providers>
</membership>