Is it legal for a 20 year old to have sex with a 17 year old even if the parents don't approve of the relationship?

In Wisconsin, if a minor is 17 years old and engages in sexual conduct/activity with an adult, the parents of the 17 year old could not file a complaint with the police requesting that charges be filed against the offending adult unless the 17 year old also wished to press charges against that particular adult. This is not the case if the minor is 16 or younger. In those instances, the parents of a minor can request that charges be filed on behalf of their child regardless if their child did not want to press charges against the adult with whom they willingly or unwillingly engaged in sexual activity/conduct. In short and to answer the question, it is illegal for a 20 year old to have sex with a 17 year old but the parents alone could not get the 20 year old criminally charged.

This depends on the State. In Michigan the age of consent is 16. In some States it is 18. It is always stupid though since it can lead to 18 years of child support payments.

No, it's not legal even if the parents "don't approve". Duh. I'm confused by your question.

Technically, it is illegal, but whether or not the prosecutor chooses to press charges, is a different issue. Because she is 17, it is doubtful that charges would be pursued.

In Texas, yes a 20 year old can have consensual sex with a 17 year old. For the purposes of sexual contact a 17 year old is no longer considered a child. See Texas Penal Code 21.11 and 22.011(a)(2) and 22.011(c)(1).