If you look at the MRT VAT one objectively, rather than based on sentiment, it’s equally daft – apart from being technically nonsensical (VAT exemption is pretty much the position now, i.e. they are in an area of work exempt from charging VAT and therefore one consequence is that they are unable to reclaim any of the purchase VAT costs they incur) it is hard to see, and there’s none on there, any justification for why Mountain Rescue teams should be singled out for special treatment over the many thousands of other charities working in many diverse fields who are burdened with exactly the same problem.
If there was a petition that proposed that, for example, registered charities should be given a more favourable treatment under the VAT regime, then that would make more sense (although still not feasible in the real world for reasons too dull and technical to go into here).
In effect, the petition is asking for the government to subsidise MRTs which, as I understand it, is not something that the MRTs actually want, or have ever asked for.