All charities are exempt from paying VAT on certain things, like advertising and fuel etc, and MR’s ability to claim back/not pay VAT on its purchases would be governed by the same rules as all other charities. You would have to change the rules for all charities, not just MR, in order to increase the scope of any relief from VAT.
Having said that, charities that offer assitance or rescue at sea are able to claim exemption on purchases of equipment, boat maintenance etc, so there might be limited scope to extend an exemption to something similar.
I thought the petition applied across the whole UK as VAT is a reserved matter.
Yep, any changes would cover the whole of the UK.