What is the ruling on one who blasphemes then performs ablution and repents before the obligatory prayer? Is he required to repeat the ablution and the prayers he performed with it? And what are the consequences for one who does that out of forgetfulness or ignorance?

Swearing at religion is apostasy from Islam. If a Muslim curses religion and then performs ablution before repenting, his ablution is invalid, because Islam is a condition for the validity of ablution and acts of worship. Consequently, his prayer with this ablution is void due to the absence of the condition of purity, and he must repeat all prayers he performed with this ablution, whether he was forgetful, ignorant, or aware of the ruling.