Yes. The non-religious argument against "gay marriage" is the argument for actual marriage, which is the permanent mating union of a man and a woman.
Unlike any other species, human offspring require about two decades of maturation and education to function as independent adults. Instead of bounding off a few days after birth to forage, human infants need long-term teaching and nurturance at the hands of both biological parents to learn the complex knowledge and skill needed for success in the human economy.
We have overwhelming sociological evidence that children thrive under the tutelage of both mother and father rather than from the limited care of a single parent. A child whose mother and father form a permanent mating relationship is more likely to be physically healthier, psychologically more stable, higher achieving in school, better able to forge good relationships with peers, and less likely to get in trouble with the law. Such children have clear, measurable advantages on almost any index of health, wealth, and success over peers raised by single parents (who are nearly always single mothers).
Given the biological and sociological realities, societies have encouraged marriage over the alternatives of indiscriminate sexual coupling or cohabitation since prehistoric times. This includes societies in southern and eastern Asia virtually untouched by Christianity, including the most populous countries in today's world. Because marriage answers a human need for stable two-parent families, it has always been a fundamental human institution.
Without strong encouragement of marriage, mating couples tend to practice cohabitation, an inherently unstable relationship that usually leaves children with only the mother's care, which is an incredible hardship for the mother and a gross disadvantage for children. Thus, marriage is needed to prevent poverty and neglect of women and children.
Homosexual coupling is one of innumerable variations of indiscriminate sexual relations antithetical to marriage. It is a particularly virulent form of sexual immorality because it rejects not only fidelity to a single mating partner, but also the heterosexual orientation on which marriage depends. Every act of homosexual orgasm conditions the participants to sexual pleasure outside of marriage, and thus militates against the sexual exclusivity that makes marriage possible.
As the permanent mating relationship of a man and woman, marriage does not require persons of the same race, but it does require partners of each sex for the act of mating. This is a biological requirement, a.k.a., a fact of life.