do they charge the sales tax at time of sale
I've bought GP items in 3 states, including one with no sales tax and each time they charged the local sales tax where the yard was located. Knowing one auction didn't include sales tax made a difference in how much I was willing to bid.
If you have a MT LLC and are registered with GP and pay from that LLC, there may be a way to exempt you from sales tax. Or maybe there's a way to recoup it later. I know this was the case some years ago, but the laws may have changed.
I found this with an online search: If Montana residents buy goods or services
online, they are not required to pay sales tax in another state. Montana does not have a sales tax exemption certificate. If you’re a Montana resident working or shopping in a state with a sales tax, and want to know about that state’s rules for exempting nonresidents from the tax, contact that state’s Department of Revenue. You cannot claim another state’s sales tax on your Montana income tax return.
GP is done online, but I don't know if the auctions count as such. Information I'm finding has some states around Montana (WA, ND) exempting residents from sales tax at least in the past, but CA is not one of them.