If you learn the sugya in the beginning of Mishnayos Keilim, not every area of Har HaBayis has the same level of kedushah and not every area is a chiyuv kareis. Some areas only require tevilah bemikvah and not haza’ah of the eifer parah adumah. Some Rabbonim have determined based on the sugya which areas on Har HaBayis one is allowed to go on after going to the mikvah.