As I see it:
Modern hetero marriage: Legitimate because it is between informed, consenting adults.
Same sex marriage: Legitimate because it is between informed, consenting adults.
“Traditional” chattel-based hetero marriage: Illegitimate because it treats women like commodities to be traded or livestock to be tamed, rather than respecting their autonomy of will. It considers their informed consent to be optional, rather than mandatory, and often denies them the right to withdraw consent and leave the relationship. It often overlaps with communities where women have their range of choices in life artificially limited by lack of education (to reduce their ability to be informed) and other cultural barriers to opportunity. It seeks to create weaknesses to provide the husband the power to exploit them for his selfish gain. It gives birth to rape culture and weakens the character of both men and women by lowering society’s standards of maturity. In the civilized world, an adult is supposed to treat his or her spouse as an equal partner, not as property.
Rape: Illegitimate because it is an act performed with blatant disregard for the victim’s consent.
The long defunct NAMBLA: Illegitimate because one member of the relationship is a child, who is considered not competent to consent by default and vulnerable to exploitation. On the related sex angle, this is also the reason it’s called statutory rape.
Child marriages in general: Illegitimate because one member of the relationship is a child, who is considered not competent to consent by default and vulnerable to exploitation. On the related sex angle, this is also the reason it’s called statutory rape.
Arranged marriages: Illegitimate because they’re not based on the consent of the members involved, but the imposition of those who wield power over them. Made worse when it’s between children.
Bestiality: Illegitimate because non-sapient animals aren’t competent to give consent. They lack the intellectual capacity to understand marriage.
Eugenics-based marriage: Illegitimate because it puts the state in control of the most private parts of people’s lives without regard to their informed consent. It’s also stupid because it’s typically reliant on pseudoscientific ideas about “purity” or “perfection” when all the evidence of biological evolution pretty much tells us there is no such thing.
Marriage by divine dictation: Illegitimate because it arbitrarily puts an unevidenced being’s alleged will above that of the involved members, typically through duress like other arranged marriages.