This is not an uncommon problem. Your sequences may be too short or otherwise lack enough information to confidently classify at genus level. You can attempt to fiddle with the classifiers, the reference database, try something like q2-clawback if you are sampling a well-studied sample type (search the forum community tutorials for more detail), or just accept that family-level classification may be the best you can achieve with the information you have.
No. These are probably real biological organisms! You could use something like
--p-include p__ to exclude those that are totally unassigned (they are most likely non-target DNA and other garbage), but sequences that can only be classified to family level are common… simply because it is difficult (or impossible!) to resolve genus- and species-level affiliation for some clades that have (near-) identical sequences for some common marker-gene targets (e.g., 16S rRNA gene V4 domain). So excluding these will SEVERELY skew your taxonomic results.
Rather, I recommend changing the “NA” label to “Other”, or else make family-level barplots.