Different taxonomic classification: with or without primers trimming

Thanks @Mehrbod_Estaki for your quick response.

I did understand the things you have already mentioned. About the feature-classifier extract-reads plugin, I used this to remove primers by following this discussion on qiime2 forum Separating two different amplicons from demultiplexed data

But, thanks for correcting me, (This plugin is meant to be used for another purpose (extracting specific region and training classifier etc)

Now my major concern is such high variability in the relative abundance of phylum (With or without primers trimming). As far as, i have understood Cutadapt worked perfectly fine as it detected 98-99% of primer sequences in my reads and removed them with (93.7% efficiency, which is great). But, when i try to compare final taxa-bar-plots of with primers and without primers (Cutadapt method), As you can see here there are huge difference in percentage of phylum median relative abundance

With Primers: p__Proteobacteria (23%), p__Bacteroidetes (31%), p__Firmicutes (31%)
Without Primers (Cutadapt): p__Proteobacteria (54%), p__Bacteroidetes (18%), p__Firmicutes (19%)

So, i am kind of scared now, as normally people say that there are not so many differences with/without primers and removing primers can only helps you to have better low taxonomic classifications (you can classify until the level of genus or even species sometimes), Correct me please if i am wrong!!.

Moreover, if i try to compare my results with other studies, its very hard to do comparison as Cutadapt method is quite new and normally 70-90% of already published data didn’t remove primers. So, if i compare my with primers results with reference studies its quite similar to them. But, if i try to be very accurate and use Cutadapt to remove primers, I know i am following right path, but on the other hands my results look strange. What do you think; Am i doing any mistake in my analysis or its normal to have at least some differences in final taxonomy with/without primers.

Any help from your side will be highly appreciated.