Is it preferable to perform the obligatory Hajj or to emigrate from a highly immodest disbelieving country to a Muslim country, if sufficient funds are available for one of them, given that the parents currently reside in this disbelieving country?

First: Hajj is an immediate obligation for whoever is able to perform it.

Second: Hijra (emigration) from disbelieving lands is obligatory if a Muslim is unable to openly practice his religion or fears falling into tribulation (fitna). It is recommendable if he is able to openly practice his religion and is safe from tribulation. If Hijra becomes obligatory and its costs prevent Hajj, then Hijra takes precedence. This is because Hijra is among the basic necessities that preclude the obligation of Hajj, and because delaying an obligatory Hijra harms the Muslim in his religion, whereas delaying Hajj is permissible with an excuse. This precedence of Hijra applies whether Hijra coincides with the time of Hajj or became obligatory before Hajj.