I'd like to add some nuance to this discussion. It is important to note that accumulative dosages is very different from short duration dosages as well as that 300mSv whole body dosage for a human is drastically different than 300mSv whole body dosage for a mouse.
Also, according to the paper 50mSv showed no affect to cognitive performance. The paper notes that Brookhaven National Laboratory can supply dose rates between 5 and 25 cGy/min, so these dosages were given over very short timeframes. This matters.
So we have somewhere between 5mSv (over ~1 minute) having no effect and 30mSv (over 1-2mins) having a statistically significant decline in cognitive performance (they did measure activated microglia in 5mSv but note that Oxygen had a different effect than Titanium). So we can clearly see that mice, in the worst case, are recovering after 24 weeks. This means the body can repair itself. This is why it is important to talk about the timeframe that a dosage was received.
So as to the 20mSv that most European countries use as total yearly dosages 1) this is well below a statistically significant measure in cognitive decline 2) this dosage is over a year and not over a minute (also likely weighted to extremities, like hands, as opposed to total body). So comparing this to radiation worker dosages is not a great comparison.
As to space flight, there are actually a lot of new rad (pun intended) technologies being developed (I worked on some of these). The primary concern in solar radiation is from charged particles (mostly protons, then alpha). These are relatively easy to block (in comparison). A lot of concern now is currently with neutrons and high energy particles. Current technologies are frequently a big chunk of titanium, kevlar, and spectra/dyneema (UHMWPE). Plastics are rather good as neutron shields because of their hydrogen density. Many of these are now being doped (boron is a common one, anyone pushing gadolinium hasn't run simulations for the energy levels we are concerned about. Or plastics doped with metals, like titanium, to increase their effectiveness against charged particles). This is a big optimization problem where layer size and order are important variables. Dopants can become charged and reradiate, but this can also be beneficial. Incoming radiation energy also DRASTICALLY changes the equation, as higher energy particles "ignore" a lot of material (see snide comment about gadolinium and thermal neutrons). It is a complicated and challenging problem for anyone interested, but importantly, we are making major improvements.
P.S. if we were REALLY concerned, you can just surround your spaceship with a large body of water. Problem is that this is heavy and extremely expensive to transport in space. The problem isn't really about can we block radiation? but can we __cost/mass effectively__ block radiation?