When I crop my target shot, it does not come out exactly rectangular. Will this effect my Camera Calibration’s accuracy?
As long as the sample squares are within the color patches on your target shot in SpyderCHECKR / SpyderCHECKR 24, there is no need for further correction.
Adjusting the alignment of the squares is usually sufficient to make this happen.
In the rare instance where your image is sufficiently distorted to not allow the sample squares to line up on top of the patches, you can either reshoot the target, being careful to shoot perpendicularly, or you can open the image in Photoshop and correct the distortion there before importing it into the SpyderCHECKR software.
For lenses which have Lens Profiles available in Lightroom, using that feature will offer lens distortion correction and will reduce darkening in the corners as well, so feel free to use that feature if you are using Lightroom, and it supports your lens model.
But keeping the target in the center of the image, instead of filling the frame, is sufficient to produce accurate results.