Might as well call this ridiculous bill (see screen shot; click to"embiggen") by a far-right Virginia State Senator Charles Carrico the "Kim Davis-Style Anti-LGBT Clerks Protection Act of 2016." Among other things, what's absurd about this bill is that the bottom line principle at stake on this issue is not complicated at all: if you applied to be a county clerk (or deputy county clerk or other public official), you are obligated to enforce the law and/or perform your duties as required by law. If you refuse to do that because you feel SO strongly that marrying same-sex couples is wrong/immoral/whatever (or, for that matter, couples of different races or religions - a Muslim and a Christian, let's just say), then you can simply resign and look for another job, opening up the job for someone else who WILL do what they're supposed to do. Voila, problem solved.
As for claiming "conscience," that's an extremely slippery slope, given that a clerk (or other public official) could cite "consience" on just about anything to avoid doing their job, whether issuing a marriage license or whatever else. Again, there are plenty of other jobs out there, nobody's forcing people to sign up to be clerks or other public officials, especially when their "conscience" doesn't allow them to perform their required duties.