Are there specific discharges that exit during a severe sneeze that are considered impure, given that I considered what came out to be vaginal discharge based on its color and texture, and I did not repeat my prayer due to my conviction that vaginal discharges do not invalidate ablution, according to the saying of Ibn Hazm and the fatwa of Sheikh Muhammad Hassan?

The obligation was to interrupt the prayer, renew the ablution (wudu'), and resume the prayer upon feeling vaginal discharge, because anything that exits from the two private parts (front or back) nullifies wudu'. No one before Ibn Hazm said that vaginal discharge does not nullify wudu'. The rule is that if you doubt whether your wudu' has been nullified or not, the default is that the purity remains. There is no necessary correlation between saying that these discharges are pure and saying that they nullify wudu'; they are pure according to many scholars, but they nullify wudu' according to the general consensus of scholars.