I do not trust them
Well, if you might have forgotten, this is a two way street. You don't trust them and neither do they trust you. You want something from them (bitcoins) and they want to sell those but they also want to be sure you are not a scammer.
Use a bitcoin ATM or do a person to person local trade. ID dilemma solved.
If you still insist on buying online and without ID, then I have to suspect a motive here. An ulterior one. Either you want to pay with questionable funds (such as PayPal or credit card) or have something more sinister up your sleeves.
If your intentions are genuine and legit and you really have concerns about your ID being misused, then the best way would be to use a bitcoin ATM or meet up locally with someone who can sell you bitcoins for non-counterfeit cash.