This is particular to a handful of alpha diversity metrics like chao1, which measure singletons — filtering singletons would invalidate those diversity metrics, but all others (like richness, PD, Shannon, evenness, etc) would be unaffected (in the sense that singletons are not used to estimate unobserved species). I believe the Bokulich 2013 paper briefly mentioned those caveats.
I recommend just sticking with other alpha diversity metrics that are not sensitive to this issue.
Note that those recommendations were made for OTU clustering. If you are using dada2 or deblur for denoising, you do not need to set an abundance filter ("the Bokulich Method"), though others on this forum have reported continuing to use that method. Either way, denoising methods do set their own filters (both remove singletons by default), so unless if you disable those filtering parameters those methods also invalidate the use of alpha metrics like chao1!
Good luck!