Here (below) is one of the referenced papers from that article, which basically asserts that the worst case long-term scenario (solar minimum) would give about the same amount of dose that the mice had in the study in about two years in space. Of course, a solar event would give a lot more dose quickly, but that is the kind of thing one can have a shelter for.
https://academic.oup.com/rpd/article/115/1-4/44/1600988
The interesting thing to me is that the dose to the mice in the study was so low, and still had measurable neurological effects. 30 cGy is not nothing, but in humans 30 cGy is about what a radiation worker might receive in 6 years at the legal limit, and is about 11 times lower than the lowest estimates for LD50/60 in humans (the amount of radiation which will kill 50% of the exposed population within 60 days). I don't normally work with mice, so I had to look up some info on them. Apparently the LD50/30 for mice varies a bit depending on strain, but it is in the range of 7 to 8 Gy. That is not that incredibly different from humans, because humans can have a similar LD50 if proper care is given.
Sources:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3743168/
https://dental.nyu.edu/content/dam/nyudental/documents/Irrad...
I don't know if the reason for the neurological effects at such low doses are because of the heavy ions used (which would be bad for space travel) or if it is because of the way it was measured in mice (not my field, I can't speak to that). But I note that airline pilots regularly receive career doses a bit lower to what the mice did (30 cGy ~= 300 mSv). And this dose is directly from cosmic rays, the same thing we are worrying about here.
Bringing us back to Sci Am: https://www.scientificamerican.com/article/air-travel-expose...