Ask yourself: what do you want to versus need to protect and why? Privacy for the sake of privacy is a waste of time, energy and other material, physical and mental resources. Formulate your threat model by spending some time with a pen and paper, answering the above question.

With that out of the way: I buy vouchers, because there is a physical retailer in my country that sells them and they are thankfully not hardcore affiliated with big tech yet. Previously, I used to pay with credit card, since PII is not saved it their payment tokens and even the tokens get deleted after six months, I believe it was.

If you need anonymity and you need to leave no trace of you having purchased Mullvad, use cash. Don't forget to put on vinyl gloves. Withdraw a vastly different amount of money from the ATM than the cost of the subscription fee in question. Deposit the envelope at a postal office - or box - not in your neighborhood.

Edit: I just recalled, that I did try paying with cash once. Worked like a charm. Naturally, there was a delay.