I'd like to see the list of activities that they don't consider wasteful spending before I pass judgments on what they do. I don't think that Republicans "hate trains," I think they view transit (be it trains, buses or anything else) as unnecessarily government subsidized and that the general tax burden could be lowered if such things were eliminated. However, that view fails to account for a major problem: that the true costs of automobile-based transportation are not assessed upon drivers. As a result, drivers are paying less than they should to drive, and transit needs to be subsidized to be competitive. To briefly use some economics terminology, the marginal private costs of driving are well below the marginal social costs of driving. If these costs were equal to each other (which would require a tax, a portion of which would go to transit/Amtrak/etc) then Amtrak/transit would require very little in terms of appropriations out of any general fund.
You see a misunderstanding of this logic when politicians argue that gas tax revenue should not be used to fund transit and only to build and maintain highways. The costs of driving extend beyond the costs of constructing roads and maintaining infrastructure, because automobile dependence results in costs to society that are not compensated for (congestion, pollution, costs of those who otherwise wouldn't need to own cars if we didn't have such an auto-centric infrastructure, and so on). The efficient, market based solution lies in a high fuel tax, a dedicated portion of which goes to Amtrak/transit. But that's not politically viable, sadly.