I understand that you may privacy-related concerns or just don’t feel comfortable about this requirement, but it is Upwork’s way or the freelance highway.
You are free to refuse to comply, but I’m afraid you won’t be able to bid, work, and get paid with an unverified account.
Now, let’s try to help you. I’m thinking about your available options.
I really don’t know what’s the exact reason for your decision. So, how about this one?
Why don’t you write a nice and totally open letter to the Upwork support team? Speak out freely and openly about your doubts and concerns. Why don’t you give them a couple of justifiable reasons to make an exception in your case? At the same time, you should provide additional information to make it possible to verify your identity in some other way. For example, you can scan your ID and passport.
Again, I can’t stop wondering why don’t you want to do it? This verification process has its limits. Upwork may ask you to verify your identity via webcam, I think they’re still using Skype for these purposes, you may comply. Then some other person may take it from there. This is a hypothetical situation. I’m not sure how often Upwork conducts identity checks once you go through the initial verification.
Long story short, if you are a freelancer with honest intentions, you shouldn’t have problems with this requirement that doesn’t last long.