That is not a scientific article. It is a lay article based on a small scale study that is not peer-reviewed. That doesn’t mean that the conclusion is necessarily false, of course.
With widespread vaccination, there will be more and more data on exactly how frequent post- vaccination infection is, how viral variation plays into this and how the three vaccines in use in the US may differ in post-vaccination infection rates. Information may also emerge on how host genetic variation plays into this, in particular the variation of HLA genes that encode proteins that allow antigen-presenting cells to present antigens to B and T cells. I’m enrolled in a study that tests for antibodies every 8 weeks after vaccination, combined with weekly questionnaires. 16 weeks out and I’ve tested positive for antibodies both times (Pfizer vaccine). Alas, they don’t give you your antibody titer!
However, it is enough at this point to know that at some level there can be infection after vaccination, so that being “fully vaccinated” does not mean you are home free. But, the likelihood is that if you are infected after vaccination, the severity of disease should be considerably reduced.
A corollary of that is that if you are infected after vaccination, you may still produce infectious virus.
A second corollary is that if you are infected after vaccination, the levels of viral replication in you will be considerably reduced, so the likelihood of the virus acquiring a mutation is also reduced. Variants are most likely to occur in patients that are highly viremic (having lots of virus) and that the primary selection for the variants will not be pathogenicity but infectivity. Of course, more infectious virus may well be more pathogenic, because the infection should spread more rapidly within your tissues after infection. It is always a race between the infection and the immune response. Your immune response has a considerable head start if you’ve been vaccinated - but more infectious variants will have an advantage - not just in their infectivity but they also may have a spike protein that does not bind well some of the antibodies elicited by the vaccine. A solution to this will be vaccine that contain sequences of variant spike proteins (and the pharma companies are already on this).
Anyway, there are plenty of good reasons to proceed with caution after vaccination - both to limit your exposure and to reduce the likelihood of your transmission of the virus to others if you are infected after vaccination.