Are you using the same binding on both? If so, try 2 seperate bindings - one for the mex endpoint and one for the wshttp:
So for the service - something like:
<wsHttpBinding><binding name="wsHttpBindingMessageUname">
<security mode="Message">
<message clientCredentialType="UserName" negotiateServiceCredential="true"
establishSecurityContext="false" />
</security></binding></wsHttpBinding>
and for the mex endpoint (no security):
<customBinding><binding name="customMex">
<textMessageEncoding>
<readerQuotas maxDepth="2147483647"
maxStringContentLength="2147483647"
maxArrayLength="2147483647"
maxBytesPerRead="2147483647"
maxNameTableCharCount="2147483647" />
</textMessageEncoding>
<httpTransport transferMode="Buffered"
maxReceivedMessageSize="2147483647"
maxBufferSize="2147483647"/></binding></customBinding>
Service endpoints will be something like:
<endpoint address="" behaviorConfiguration="Server.Services.DefaultEndpointBehavior" binding="wsHttpBinding" bindingConfiguration="wsHttpBindingMessageUname" name="DefaultHttp" contract="Server.Services.IMyService" listenUriMode="Explicit" />
<endpoint address="mex" binding="customBinding" contract="IMetadataExchange" name="" bindingConfiguration="customMex" listenUriMode="Explicit" />
With this setup, it's not applying the security for mex so you shouldn't get that message when trying to update service reference. Either that, or create another secure binding that uses different credentials, i.e. a client certificate on your machine.
The following MSDN post has a sample of this and more info can be found on this blog regarding secure mex endpoints.