Point values obtained from rasters with different extent, projection and resolution

I am trying to predict a species’ distribution. I am fairly new to GIS, so apologies if I am talking nonsense.

I gathered various geo-referenced environmental data from different databases. The files come in slightly varying extents (global scale), most have WGS84 projection but some do not, and generally the resolution varies between 250m to 1km. I have around 500k occurrence points and intended to sample 500k points randomly as background data. I read that reprojecting rasters should be avoided at all costs and instead the spatial points should be reprojected to the CRS of the particular raster file before extracting values.

I just started reading the introduction to species distribution models by Robert J. Hijmans and Jane Elith who note "For any particular study the layers should all have the same spatial extent, resolution, origin, and projection.". I was a bit surprised to read this as I did not see any harm in extracting point values from different resolutions, extents and projections (as long as points are reprojected).

I hope there are more experienced GIS modelers here that could enlighten me whether I was too naive in simply extracting point values from all these different databases without worrying about harmonizing all the rasters to the same extent, resolution and projection.