UPDATE
So my Context Service now starts and using DEBUG I can see the following in it's logs:
2017-03-22 08:57:26,460 DEBUG VariableResolverUtil - Found parameter: ${oauthenabled:-true}. Resolved value: true
So I assume OAuth is on for the Context Service.
I found the same line when logging the Discovery Service and Content Services.
Everything looks ok.
One confusing thing I did notice is and error logged against the ContentServiceProvider in the cd_client.log:
2017-03-22 9:28:40 DEBUG [Sdl.Web.Delivery.ADF.HttpModule..cctor] - Ambient Data context initialization.
2017-03-22 9:28:41 DEBUG [Sdl.Web.Delivery.DiscoveryService.DiscoveryServiceProvider..ctor] - Attempting to construct discovery-service provider.
2017-03-22 9:28:43 DEBUG [Sdl.Web.Delivery.Service.OAuthTokenProvider..ctor] - Using token-service: http://10.10.1.132:8082/token.svc
2017-03-22 9:28:43 DEBUG [Sdl.Web.Delivery.Service.OAuthTokenProvider.CreateOrRefreshToken] - Attempting to get token from token-service.
2017-03-22 9:28:43 DEBUG [Sdl.Web.Delivery.DiscoveryService.DiscoveryServiceProvider..ctor] - Finished constructing discovery-service provider.
2017-03-22 9:28:43 ERROR [Sdl.Web.Delivery.ContentService.ContentServiceProvider..ctor]
Problem authenticating with service. Please make sure your authentication settings are correct and you have enabled authentication.
But the error is still coming from the ContextServiceClaimsProvider in site.log (shown above).
I guess this is the same root cause?