Hindu tradition has always recognized a variety of ceremonies as valid marriages, several of which have no kanyādāna. In other words, "random people" have always contracted marriages according to personal tastes, and Hinduism has given a veneer of religion to whatever society was already doing. The alteration of Hindu traditions by critical thinking is not a threat; rather, it is the salvation of a religious identity that would otherwise become obsolete.
Ancient Hindu law books list eight types of valid marriage ceremonies: Brāhma, Daiva, Ārṣa, Prājāpatya, Gāndharva, Āsura, Rākṣasa, and Paiśāca.
- The Paiśāca type is illegal under the Hindu Marriage Act of 1955, as it is the explicitly non-consensual violation of a sleeping or drugged female.
- Rākṣasa marriage would be illegal in its original form, abduction of an unwilling female, but legal in its modern form, elopement followed by willing cohabitation.
- Āsura marriage, buying the bride from her family as an alternative to kanyādāna, unambiguously objectifies her.
- Gāndharva marriage has no kanyādāna, no priest, no witnesses - just mutual consent between the couple.
- In Prājāpatya marriage, there is no kanyādāna because the bride remains a member of her parental family.
- Ārṣa marriage exchanges the bride for a pair of cattle instead of doing uncompensated kanyādāna; a cow was essential for a family's survival, and a wife was even more essential.
- Daiva marriage designates the bride as dakṣiṇā rather than dāna, as her family invites a scholar to perform a ceremony for them, and rewards him with the bride as a token of gratitude.
- Only in Brāhma marriage is there kanyādāna: the bride's family yields her to a worthy groom without receiving anything, simply to fulfil their duty as parents.
The Hindu Marriage Act of 1955 affirms the validity of any consensual marriage ceremony that accords with the tradition of either party to the marriage. It does not require kanyādāna at all. The only ritual that makes marriage legal is saptapadī, and even that is optional, as the law declares that if the ceremony includes saptapadī, the marriage takes effect when the seventh step is completed. If there is anyone insisting that kanyādāna is integral to Hindu marriage, that battle was lost 68 years ago.
Several people commenting in this topic have singled out the bride's father as the one giving her away. As far as I know my community's traditions, kanyādāna is always performed by an opposite-sex married couple. The father is ineligible to perform this ritual in the absence of his wife (although in an emergency, he is permitted to use an areca nut to represent his like-minded wife). The bride's relatives may invite any respected married couple (related or unrelated to her) to perform kanyādāna, without implying that the bride is anyone's property to be given away.
Finally, I would like to point out that the words used for kanyādāna do not use the names Lakṣmī and Viṣṇu/Nārāyaṇa. The words are "asmai Śrīdhara-rūpiṇe varāya mama Śrī-rūpiṇīṃ kanyāṃ" - to this selected one representing the Bearer of Śrī, my girl who represents Śrī. Thus, the bride is equated with Śrī - excellence or distinction, not material prosperity per se, and she is given to the groom because he is worthy of bearing that honour.
I see nothing wrong with giving the groom to the bride in the same manner, or giving two brides to each other, or two grooms to each other. If Hindu tradition has something good to offer, let any couple take the benefit of it.