QGIS 2.18.24 – which I use for work and cannot update – seems to struggle with some WMS and WMTS layers. They seem to render at an incorrect resolution, although they appear aligned properly. This is Mapbox (WMS): And this is esri World Topo (WMTS): As you can see (click to enlarge), both look really crappy. Seems like the resolution is way off. Other layers do not have such issues. Am I missing something obvious here?
I'd strongly suggest that you ask your IT team to consider allowing you to have at the least a parallel install of QGIS 3.4LTR or QGIS 3.10, as they've made inumerable significant improvements in every area since 2.x, not least of which was a change to the raster rendering pipeline that allows for pixel-perfect rendering at native resolution, which did not occur in prior releases, as the raster data were still being scaled (resulting in the distortions you see in your imagery).
For your specific case, you might be best off to convince your IT team to wait for QGIS 3.10LTR, which should be out soon (2020-02-21), as this change has been committed to QGIS Master, 3.8, 3.10, and 3.10LTR, with no evidence of being backported to any other release.
Changelog for QGIS 3.8:
Feature: Improved “Zoom to Native Resolution” behavior
We’ve improved the “Zoom to Native” action, so it now works correctly with tiled (e.g. WMTS/XYZ/ArcGIS MapServer) layers, by zooming to the closest native tile resolution. Additionally, we tweaked tile rendering so that pixel-perfect rendering occurs when the map is viewed at a native tile resolution. The result: super-crisp map renders when using tiled layer sources!
Summary QGIS 3.8 and newer have the improved raster rendering logic which will allow for pixel-perfect rendering, even of webmap layers.