If the parents are Muslims, they should not prevent their children from performing obligatory worship, but if they try to do that for any reason, you must perform your obligatory worship at any cost. If Muslim parents object on recommended worship, you have then to consider not to hurt their feelings and not to make them feel disrespected, specially when their objection on the recommended acts is based on their fear on you or care for you because of their thinking that certain recommended worship can affect your health such as recommended fasting. You should do your best to keep the respect of your parents and avoid any act which might cause them feeling disrespected.

If the parents are non Muslims and try to stop you from your Islamic duties, you are then not obliged to listen to them as no one is entitled to stop us from our obligatory duties.
In anyway you should always keep the respect of our parents even if they are non Muslims. In Quran Allah says in Surah Luqman, verse 15 [But if ( Your parents) strive with you to make you join in worship with Me others that of which you have knowledge, then don't obey them; but behave with them in this world kindly]

Wassalaam