If the activity is illegal, the question of whether consent can be effective is primarily one of criminal law, not of tort law. For example, the principle that a sufficiently young person cannot consent to sex with an adult is a matter of criminal law, and such sex is a criminal act, not merely a tort, although I suppose it might also be a tort. Note also that there is an "age of consent" above which a person may consent to a marriage, and presumably to sexual activity within the marriage, and this is often younger than the age of majority. For sexual activity outside of marriage, the age will be specified in the law on statutory rape (which may go by another name), and may or may not be the same as the age of consent to marriage, and also may not be the same as the age of majority. See This Wikipedia article and this linked article. The legality of sexual activity when one partner is under the local age of consent will in many jurisdictions depend on the age of the older partner, and the difference of age between the partners. These are known as "Romeo and Juliet laws"
In many other cases part of the essence of a tort is that it is an act done without consent, or even against the will of the damaged party. For example making a copy of a copyrighted work is copyright infringement which is a tort (and can also be a crime, although it is rarely treated as such) unless that act is authorized by the copyright holder or the holder's delegate, in which case the act is fully legal.
In short, this is going to vary not just by jurisdiction, but by the particular tort or crime involved, and will be sufficiently complex that speaking of a "majority rule" is probably not meaningful.