Astronauts exposed to essentially exactly the same rate of radiation exposure on LEO missions as where they traversed the van allen belts and walked on the lunar surface outside the protection of the magnetosphere
No one has claimed that astronauts in LEO have the same rate of radiation exposure as those who went to the Moon. We said that the exposure to
electromagnetic radiation is the same in LEO as it is in cislunar space. That does not include
particle radiation, which we never got around to discussing.
surviving 1600 x ray flares and many hundreds of par tile events...
How many of those flares produced radiation exposures that were of biological significance? I'm not interested in speculation, please provide numbers.
THEY GOT REAL LUCKY, they "won the lottery" so to speak.
That is a gross mischaracterization of the actual situation. The Apollo spacecraft was well protected from Van Allen Belt radiation and normal cislunar radiation. The only real threat was from
major solar flares, which are rare. The Solar Particle Alert Network was established to support the Apollo program. SPAN's function was to monitor solar activity during the missions and provide warnings of particle events. The network included seven stations around the world, situated so as to provide 24-hour coverage of the Sun at both optical and microwave frequencies. If SPAN detected that a large solar flare was imminent, there was a few hours' advance notice of the particle flux. This was adequate time for the astronauts on the Moon to get back to the LM, take off, rendezvous with the CSM, and take cover as best they could. While in lunar orbit, the Moon would protect the astronauts for half of each orbit. At other times the spacecraft would be turned so the bulk of the service module was between the astronauts and the incoming particles. The astronauts had a handheld Geiger counter so they could find the safest spot in the command module cabin should they have to ride out a solar flare.
45 years later it cannot be done
That's only because nobody currently has a moon-capable system in production and/or operation. It's not because it is impossible or because we don't know how to go to the moon.
no government claims it is near ready ebcause they don't have the means to get beyond the magnetosphere and protect astronauts from radiator in space
When has any government has said that a short duration Apollo-style mission to the moon is impossible due to radiation (or for any other reason)? Provide sources.