Sie müssen beide Konfigurationsabschnitte beibehalten, so
<system.data>
<DbProviderFactories>
<remove invariant="System.Data.SQLite" /> <add name="SQLite Data Provider" description=".Net Framework Data Provider for SQLite" invariant="System.Data.SQLite" type="System.Data.SQLite.SQLiteFactory, System.Data.SQLite" />
<remove invariant="MySql.Data.MySqlClient" /><add name="MySQL" description="ADO.Net driver for MySQL" invariant="MySql.Data.MySqlClient" type="MySql.Data.MySqlClient.MySqlClientFactory, MySql.Data"/>
</DbProviderFactories>
</system.data>
<entityFramework>
<providers>
<provider invariantName="System.Data.SQLite" type="System.Data.SQLite.SQLiteProviderServices, System.Data.SQLite.Linq, Culture=neutral, PublicKeyToken=db937bc2d44ff139" />
<provider invariantName="MySql.Data.MySqlClient" type="MySql.Data.MySqlClient.MySqlProviderServices, MySql.Data.Entity.EF6"></provider>
</providers>
</entityFramework>