And who is equipped to be the ultimate arbitrator and judge of all truth?
Of all truth? I don't think anybody. But there are some things we generally can agree on. This world exists outside of our own minds (unless you want everything to dissolve into Solipsism. I know I don't.) So if we accept that, then we can have a rational discussion about that world.
I have a chair made from the wood of a walnut tree. Someone who claims otherwise is wrong.
1+1 = 2
bacteria and viruses and parasites, combined with our bodies immune response cause illness, not bad humours, and insufficient trepanning.
Gradually we begin to lay a groundwork for objective reality. Someone who claims that the stars are velcro'd to a giant black rug in the sky at night, is wrong. Some things are true and others are not.
Science provides us with many tools to evaluate claims about the world around us, and when it is demonstrated to be wrong, it is corrected. Philosophy provides us with some tools, as well. As does logic, art, mathematics, even theology.
One can make any claims about the world around us they wish, but their evidence should be weighed and compared against the claims of others, and a decision is made based on the weight of evidence - usually by some type of consensus between independent evaluations (regardless of field).
They are not inherently equal claims - they are only as good a claim as the evidence that supports them.
We can have a larger conversation about what constitutes reliable evidence, but to say that all claims are equally valid, is plainly incorrect. We may not be able to know absolute truth, but we can know objective truths. And we ignore them at our peril.