There are two kind of radiation that the astronauts traveling to Mars will have to overcome. First there are cosmic rays that travel at near-light speeds. Second, there are more subdued nature of radiation from the solar activities.
The travel to Mars will take an estimated three year mission time. That is enormous amount of time for survival of humans given the amount of radiation in outer space. Radiation expert Ron Turner, a senior science adviser at NASA’s Institute for Advanced Concepts in Atlanta told recently to Smithsonian (https://www.smithsonianmag.com/science-nature/radiation-remains-problem-any-mission-mars-180959092/) that doubling the thickness of the spaceship hull only reduces the radiation for astronauts by only 10%. This is major issue for the Mars mission. The only way to circumvent this is to shorten the Mars mission time. This option may not be ready till we reach Type 1 civilization’s technological level where a worm hole can be used for space travel.
The biggest issue comes from another corner of the space travel spectrum. What if some extraterrestrial civilization continues to control the cosmic rays that travel at near-light speeds? In that case no matter what our mission do to cope up with radiation, manned mission cannot be possible unless we reach Type 1 technology and use space-time manipulation with gravity waves to use a worm home for traveling very fast into any planet, solar system, or galaxy.
Hence, there is a possibility that Mars travel may not be possible like moon mission is NOT since seventies until we reach much higher technological maturity as a civilization.