Hi @owlpen,
I would not be surprised that you are amplifying mostly boar host DNA given that you are working with boar semen. Primers, in PCR, often amplify whatever they can, if there is nothing better to bind to... I've had a case in which, the V4 16S rRNA primers amplified 12S rRNA gene sequences, quite well, some samples were dominated by them and hardly any 16S rRNA etc...
Given my experience I noted above. I wonder how many of these mapped reads are actually bacteria? Probably not many, but could be worth investigating. Also, what are you using as your reference database to assign taxonomy? I would also like to know what variable region you are targeting.
It shouldn't. At least you should be preparing your data so that only the amplicon sequence is present. That is, the PCR primers and adapters, etc.. should be removed prior to denoising. The common approach is to use cutadapt to remove the PCR primers from the reads (if the sequencing protocol sequences through the primers). Then send to DADA2, etc...
If you had a time machine 
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Often, to mitigate off-target amplification, you can make use of touch-down PCR. that is, you can start with an annealing temperature that is ~ 8-10 C higher than your target. Then drop 1 C each cycle until you hit your target. Then go for another 20 cycles or so. The idea is that your ideal targets are more likely to preferentially bind to your primers at higher temperatures, thereby pre-amplifying those targets. Reducing off-targets. This does not always work...
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The more common thing to do, if you are unable to change primers, is to use blocking primers or peptide nucleic acids to block host DNA amplification. See this post.