I know very little about the 1800s outside of European warfare. Was railway technology really advancing so rapidly in the United States that missing the mark by a mere 20 years and a few hundred miles counts as an anachronism?
From Stephenson's Rocket in 1830 to Mallard (still current World Steam Speed Record) in 1938, trains were changing rapidly. Rail was being built out everywhere, as fast as possible. From 1830 to 1900 they were the cutting edge of human travel technology, that only really transferred elsewhere with the rise of the car, tram and bus in the very late 1800s, but mainly 1900 on. Fast travel was a new big deal in comparison to the slow discomfort in a coach that had preceded them. Even with an efficient network of coaching inns, and fast team changes, they were expensive, slow, uncomfortable, and unheated.
Competition was intense - by 1900, the UK had a couple of hundred train companies, many in parallel competition with competing lines, sometimes competing stations in the cities too. 20 years could easily be the equivalent of 5 or 10 years of computing in the 1980s or 1990s. We'd immediately pick up similar anachronisms in halt and catch fire, or the latest hacker movie. Or loads of 1940s or 1970s cars in a movie set in the 60s.
As a European, train emoji just look odd for being wild west, as they're so unlike the common European designs (mainly from the cow catcher and silly funnel shape).
Would a Minié rifle be an anachronism in the Franco-Prussian War, only 20 years and a few hundred miles from the Second War of Italian Independence? (Yes, the Austrians discovered that they were outdated compared to the Prussian guns, and so the French retooled to the chassepot rifles instead.)
It's not so much the fact that the technology was wildly obsolete as it is the fact that there are distinct visual styles that are localized to particular places in certain eras. If you know what those are, seeing people get it wrong can be quite jarring. Imagine a scene supposedly set in Ancient Rome where one character shows up in Prussian court dress.
But your statement is about purchases, rather than common use. Just because 4-6-0 locomotives were being purchased then, it certainly doesn't follow that you wouldn't see any 4-4-0 locomotives in 1870, does it? Especially since 4-4-0s were still being built in the US as late as 1893 according to Wikipedia [1].
Also "wild west era" is pretty vague to start with and can be considered to cover almost whole 19th century. So the specific situation at 1870s might not be even all that relevant
I don't know a lot about trains in particular, but mechanical technology was advancing very rapidly during this period. It's roughly when the mass production of interchangeable machine parts started to take off. Singer (sewing machines) and Colt (revolvers) are two notable examples.
