Nope, you cannot be a conservative at all if you espouse other than conservative values.
Like being a little pregnant, that dog don't hunt.
That's simply bullshit. I've never claimed to be a social conservative. But there is a proud tradition of conservatism that is secular, that is concerned with individual liberty and Constitutionally limited government (including when it comes to the bedroom), and emphasizes such things as economic growth and national security.
But it's more than likely correct that you cannot be a social conservative without also being a bully. Take your meddlesome religious dogma and, in INVAR's words, stuff it!