Mt first instinct was to check the data of the sweeping generalisation. You don't specify which tax, but for the purposes of simplicity I'll assume that you're referring to income tax. In which case, a 3% increase to income tax would raise around £18bn.
Just to put things into perspective rather than have dramatisation for effect. I'm sure you can do the maths and calculate what increase in tax is needed to make your example more accurate.
But while I'm here, is there anything else you'd like to be able to opt out of paying tax for?
Also, if there are indeed benefits to the royal family, how do we opt you out of those? Perhaps increase your income tax to compensate?
Devil's advocate.
According to other sources in this thread, it seems we pay no income tax at all. Why then is the 50p a day per person bandied about by the media.
In terms of opt outs - you can opt out of your 2nd pension and the deduction disappears from your payslip. You can opt-in to salary sacrifice for childcare vouchers and the amount appears on the payslip. Why not introduce the RST (Royal Super Tax) in addition to the NI contributions which appears on the payslip and make it optional where opt-outs are concerned. Just a thought since you asked.