Safe depends on the person's unique physiology
I ride a fs mountain bike and i do steep climbs and long downhiling. I usually don't need to stop to rest (i usually go 20-60km) but when i am climbing very steep paths, my heart rate is very high, like 180bpm (i am saying about continuous climb from 500m altitude to 1100m). I do not feel "tired" (i mean, i can continue without having to stop, but my bpm is high in steep climbs). Is this normal?
Everyone is different, and as such everyone will have a unique capacity to work at various HR's, and under various activities. I race 2x/week - once a week in a 30km road time trial, and once a week in a 12km MTB race. In the road time trial my average HR is usually 185ish, with a max of 190-192. The MTB race is a different story though...it is common for me to have an average HR of 192-195, and my max HR's are always over 200. I've maxed out at 207 this year.
I'm 32, and in good (not fantastic) shape. Using the 220-age formula, my max should be 188, but I quite often go 200+. The formula is obviously a loose estimate, and doesn't take into account lung volume, ability to buffer lactic acid, or efficiency in which your body transfers and utilizes oxygen. Some people may pass out working at HR's of 185 because their body is running into an oxygen debt. I can ride above 190 for a few hours without going anaerobic. I don't consider myself to be in great cardio shape, but somehow my body is good at transporting and utilizing oxygen...must be genetic, because it's not from hard work!!!
My wife is in incredible shape (triathlete and marathoner), and has a genetically large lung volume which lets her work at high heart rates before going anaerobic. In a MTB race she will often reach HR's of 195-200, with averages between 185-190.
Different people have different buffering capacities, and therefore can work at different heart rates before going anaerobic, and consequently passing out or having to stop. A major indicator of this efficiency is not just how high you can work at, but how quickly your heart rate returns to normal.