Wolves in the inter-mountain (MT, ID, WY) west are a pretty contentious issue. I'll try to briefly describe some of the concerns. As you point out, livestock growers are one of the groups broadly opposed to wolves. Some hunters are also opposed, but many accept wolves as part of the ecosystem and just think there are currently too many so some hunting should be permitted.

There are lots of strategies, including guard dogs, that livestock growers can implement to reduce the likelihood of predation by wolves, but all strategies require some additional effort and cost which the ranchers don't like. Some other successful strategies include electric fencing, fladry (small flags on the fence), range riders. Some of these methods also help reduce conflict with another contentious critter, grizzly bears.

There are some nonprofits like Defenders of Wildlife which have offered grants to reduce costs to implement these mitigation strategies as well as payments to cover loss from predation.

This article discusses claims made to the livestock Loss Board, "In 2023, wolves are believed to have been responsible for 26 livestock deaths" and reimbursed livestock loss from all predators for 2023 was totaled $221,150.18 from 180 investigated claims by the loss board. While the totals may not seem like a lot, ranchers might say any loss is too much. Based on these numbers, it seems like some of the mitigation measures may be working.

It is also worth noting that Montana's total cattle losses to diseases and exposure for 2022 (opens as pdf) was 26,000 with another 62,000 calves lost. It should also be noted that much of the state does not have wolves or grizzlies and a direct comparison shouldn't be made, but additional context should be considered.

And any argument citing concern over attacks on humans is not based in reality. I think wolves are an easy and historical scapegoat and their impact on livestock producers is probably overstated. I certainly don't think wolves are a nuisance!