>I really find it hard to believe you can compare temperature measurements “globally” before 1950s with any sort of consistency
You're right to be skeptical and we can't. There isn't even a single "global temperature" today. There is, for example, a global surface temperature measured by satellites and ground stations, except where there is cloud cover and no ground stations. It is extrapolated in such places based on mathematical models. Also a satellite passes only so often across certain area (or takes low resolutions photos if at geostationary orbit) so data is further extrapolated in time. And that is only the surface. What about the depths of the oceans and the thickness of the atmosphere? Is this what is meant when they make claims like "hottest 12 months" on record? If yes, it tells you nothing about true "global temperature".
"Global temperature" today is a mathematical construct, a model based on limited sensor data. A LOT is extrapolated in that model. How exactly you do that affects the results you get.
We don't have consistent measurements across the thickness of the atmosphere and depth of the oceans. There are sporadic measurements, like satellite measurement of cloud cover temperature and knowing how high this cloud cover is, but what's going on below and above? It's all filled in by "the models". Models people wrote to behave how they expect they should behave.