Backwoodsman....Your hypothesis does not bear scrutiny. As discrimination and stigma against homosexuality has diminished and Civil Union / Homosexual "marriage have been adopted, in the last decade, male homosexual infection rates have rocketed in tandem.
They now stand unbelievably at over 70% of all new male sexual infections for HIV, Syphilis and most other STDs in the US.
In the UK, the health agencies have stopped releasing figures by demographic, simply stating that MSM are the largest "at risk" group and that HIV infections are falling.
This is concealment of the facts, and is un-beneficial to society AND homosexuals.

I do not think that homosexual "marriage would CAUSE health problems, the health problems are already there in epidemic proportions.

The problem with homosexual "marriage" is that the rule book has been torn up, marriage now often involves "open" relationships with two main partners and several sexual partners on each side.
That is the trouble with redefinition, where does it stop? what about monogamy, what about a secure foundation to raise children....who will now define what type of sexual arrangement is suitable for the rearing of children....and where do the children themselves fit in, do they not deserve the chance of a mother father and extended family?
These "open relationships are a real hazard as far as sexual infection is concerned.