Update 3/28/2018 - This didn't work after I installed MySQL 6.10. I'm still getting the issue, unfortunately.
Update 8/25/2018 - Fixed!
MySQL is updating their RDBMS to 8.1 to add in some TLS1.2 support. Since I'm updating all my MySQL programs, I installed the newer Connectors on my machine. Yep, you guessed it. Broke Visual Studio again. What I did this time was download the newer Visual Studio plugins (even though I really don't use them), and this fixed the constant errors of the plugin being broken.
You can download it from here: https://dev.mysql.com/downloads/windows/visualstudio/
Hopefully it will help others from scratching their heads who, like me, may have been using the older, buggier plugin.
Below is my previous attempt to fix this issue. I'm keeping it here so others may find this page if they're searching for the Visual Studio errors.
So, I was updating my MySQL Connector driver from 6.5.7 to 6.10.6. I had a number of Visual Studio instances opened, so when it asked me to close them all, or do a reboot later, I took the 'I'll reboot later' path. I wonder in retrospect if it would have made my outcome better. So I got the new MySQL connector drivers installed, closed up, and did a reboot. However, whenever I would start VS, I would get a dialog box pop up telling me that the MySQL 6.5.7 plugin wasn't able to be loaded. It said I could in the ActivityLog.xml file for more information. It gave the path to the file: C:\Users\troy.tudor\AppData\Roaming\Microsoft\VisualStudio\11.0\ActivityLog.xml. So I opened it up with TableViewer, sorted by the 'type' column, and found the Error entry:
System.IO.FileNotFoundException: Could not load file or assembly 'MySql.VisualStudio, Version=6.5.7.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d' or one of its dependencies. The system cannot find the file specified.
File name: 'MySql.VisualStudio, Version=6.5.7.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d'
at System.Reflection.RuntimeAssembly._nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, RuntimeAssembly locationHint, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
at System.Reflection.RuntimeAssembly.nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, RuntimeAssembly locationHint, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
at System.Reflection.RuntimeAssembly.InternalLoadAssemblyName(AssemblyName assemblyRef, Evidence assemblySecurity, RuntimeAssembly reqAssembly, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
at System.Reflection.Assembly.Load(AssemblyName assemblyRef)
at System.ComponentModel.Composition.Caching.ReflectionResolver.ResolveAssembly(String assemblyName, String codeBase)
at System.ComponentModel.Composition.Caching.AttributedModel.ReflectionCacheServices.ReadAssembly(CachedAssemblyData assemblyData)
at System.ComponentModel.Composition.Hosting.CachedAssemblyCatalog.get_Assembly()
at System.ComponentModel.Composition.Hosting.CachedAssemblyCatalog.<.ctor>b__0()
at System.ComponentModel.Composition.Caching.AttributedModel.ReflectionCacheServices.<>c__DisplayClass6.<GetLazyTypeForPart>b__5()
at System.Lazy`1.CreateValue()
at System.Lazy`1.LazyInitValue()
at System.Lazy`1.get_Value()
at System.ComponentModel.Composition.Caching.AttributedModel.ReflectionCacheServices.<>c__DisplayClass9.<GetAccessorsFromCache>b__8()
at System.ComponentModel.Composition.ReflectionModel.LazyMemberInfo.GetAccessors()
at System.ComponentModel.Composition.ReflectionModel.ReflectionExtensions.ToReflectionMember(LazyMemberInfo lazyMember)
at System.ComponentModel.Composition.ReflectionModel.ReflectionExtensions.ToReflectionWriteableMember(LazyMemberInfo lazyMember)
at System.ComponentModel.Composition.ReflectionModel.ReflectionMemberImportDefinition.ToImportingItem()
at System.ComponentModel.Composition.ReflectionModel.ReflectionComposablePart.GetImportingItem(ImportDefinition definition)
at System.ComponentModel.Composition.ReflectionModel.ReflectionComposablePart.GetImportingItemFromDefinition(ImportDefinition definition)
at System.ComponentModel.Composition.ReflectionModel.ReflectionComposablePart.SetImport(ImportDefinition definition, IEnumerable`1 exports)
at System.ComponentModel.Composition.Hosting.ImportEngine.PartManager.TrySetImport(ImportDefinition import, Export[] exports)
at System.ComponentModel.Composition.Hosting.ImportEngine.TrySatisfyImportSubset(PartManager partManager, IEnumerable`1 imports, AtomicComposition atomicComposition)
at System.ComponentModel.Composition.Hosting.ImportEngine.TrySatisfyImportsStateMachine(PartManager partManager, ComposablePart part)
at System.ComponentModel.Composition.Hosting.ImportEngine.TrySatisfyImports(PartManager partManager, ComposablePart part, Boolean shouldTrackImports)
at System.ComponentModel.Composition.Hosting.ImportEngine.SatisfyImports(ComposablePart part)
at System.ComponentModel.Composition.Hosting.CompositionServices.GetExportedValueFromComposedPart(ImportEngine engine, ComposablePart part, ExportDefinition definition)
at System.ComponentModel.Composition.Hosting.CatalogExportProvider.GetExportedValue(CatalogPart part, ExportDefinition export, Boolean isSharedPart)
at System.ComponentModel.Composition.Hosting.CatalogExportProvider.CatalogExport.GetExportedValueCore()
at System.ComponentModel.Composition.Primitives.Export.get_Value()
at System.ComponentModel.Composition.ExportServices.GetCastedExportedValue[T](Export export)
at System.ComponentModel.Composition.ExportServices.<>c__DisplayClass11_0`2.<CreateStronglyTypedLazyOfTM>b__1()
at System.Lazy`1.CreateValue()
at System.Lazy`1.LazyInitValue()
at System.Lazy`1.get_Value()
at Microsoft.VisualStudio.Text.Utilities.GuardedOperations.InstantiateExtension[TExtension,TMetadata,TExtensionInstance](Object errorSource, Lazy`2 provider, Func`2 getter)
WRN: Assembly binding logging is turned OFF.
To enable assembly bind failure logging, set the registry value [HKLM\Software\Microsoft\Fusion!EnableLog] (DWORD) to 1.
Note: There is some performance penalty associated with assembly bind failure logging.
To turn this feature off, remove the registry value [HKLM\Software\Microsoft\Fusion!EnableLog].
I highlighted a couple key bits of information that helped me get the irritating dialog box from popping up every time I opened a project. In the Registry Editor, I searched for the Public Key Token: c5687fc88969c44d. I found it embedded in a number of key GUIDs, but then the search landed upon a value in [HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Fusion\GACChangeNotification\Default]. There I found the value "MySql.Data.CF,6.5.7.0,,c5687fc88969c44d,Yes,MSIL"=hex:8d,b1,1d,fc,76,c1,d3,01. I exported the Default branch so I'd have the key value to re-enter in the event that it hosed something else up, deleted the key, and started Visual Studio. When I opened my project, no more error dialog box. Cool!
So if anyone else has been stumped by this problem, hopefully this will help you resolve it.