作为实意动词，do一般是及物动词，偶尔也有不及物的用法。表示“做”的概念时，do一般应跟一宾语。你刚才的句子，似乎改为You must do it (everything) as your parents tell you to.更符合语法。但在实际语言中，尤其在类似你的例句中，即含有一方式状语从句as的时候，do后的宾语往往省略，可能因为要做的这个宾语比较模糊，或者不易说出。例如：

In that event you must do as he says. 如果那样的话,你必须按他说的做。

I must do as my father wished before he died. 我必须按照我父亲去世前的意愿行事。

Soldiers must do as they are bidden. 军人必须服从命令。

They who cannot do as they will, must do as they can. 不能遂所愿, 亦当尽所能。

You must do as you are told , whether or no. 总之,你必须按照吩咐的去做。

You ought to do as your teacher tells you. 你应该按老师说的做。

I have no choice; I must do as he tells me. 我没有选择的余地, 只能按他说的去办。

You must do as you please. 你必须做你喜欢的事。

We must do as Lei Feng did. 我们要像雷锋那样做。

You must do as you are told. 你要照吩咐行事。

I'm in charge of your class tomorrow, so you must do as I tell you.明天我负责你们班，因此你要照我说的去做。

You must do as you think fit.你认为怎么合适就怎么干。

总之，语言在向着简洁的方向发展，所以，适当的省略而不引起歧义，是可以接受的。