Hi @Brigitta1,
I guess the effect on the primer in the sequences may vary depending on what tool do you use for the taxonomic assignment, and what settings do you use. However, any artificial sequences may create fake similarity which should be considered false positive matches.
As for me, I do like to remove any non-biological sequences as very first step,
so I know there are no effect on this. For example, the presence of primers in th edenoising step may result in the production of two alternative ASVs for a given amplicon, which would have not be produced if primers were removed (remember that sequences differing by a single bases are called as separate ASV by dada2).
Altough these ASVs amy be still assigned to the same species, you will end up on overestimating the alpha diversity for that sample.
A thread you may waht to look at is the following:
(which I totally forgot I was involved ...).
Hope it helps
Luca