VAT goes to the Treasury. It is not specifically to pay for the EU, except to the extent that it contributes to the government's general pot of money that the UK's contributions are paid out of. VAT is harmonised across the EU, but individual governments have some degree of latitude in setting the applicable rates, within the legal framework set out by the EU (and which, at the risk of getting political, the UK had a part in agreeing). It is true that after Brexit the UK government will be entirely free to set whatever rates it wishes, how that will work out remains to be seen.

What this seems to mean in practice is that post-Brexit we will now be able to purchase stuff VAT-free from businesses in the EU, including musical instruments and equipment. Great! However we will have to pay UK VAT (or whatever replaces it) together with import duty when it comes into the UK. What these rates are will depend on what deal we eventually agree with the EU, until then (as I understand it) they will be at WTO rates. Whether this works out more or less expensive for the purchaser remains to be seen, it will certainly add to the paperwork and delay in receiving your order. It will make it less attractive to buy from companies in the EU, and with less competition UK prices may then rise. It will significantly affect trading of second-hand instruments, especially by private individuals who do not currently have to charge VAT.

There's an interesting article here:

Impact Assessment: Brexit and the musical instrument market

Musicians taking CDs and other merchandise into the EU for sale will be subject to the requirements I linked to before to pay HMRC up front.

Digital sales must now charge VAT at the applicable rate in the purchaser's country, and unlike physical products there is no VAT threshold so this applies to all sales no matter how small. There is a system known as VATMOSS which was being set up to administer all this, so it would be handled through HMRC rather than having to deal with separate EU countries, but I'm not sure if this will continue after Brexit. Many musicians sell downloads through portals such as CD Baby and Bandcamp, which handle the VAT for them so the impact may be fairly small.