There is some truth to that, but with age and experience, people also change their viewpoints on many things. I suspect you are right in part, not so much because it is just ‘old people’ that have this opinion, but other factors. For one, younger generations - 50 and under - are much more likely to have gay people in their social circles. This was not true in earlier generations. Regardless of personal opinions on the issue, it becomes personalized as people we know that are directly asking for it. My parents knew few outwardly gay people, whereas people in the younger and middle generations have many friends.
There is also a libertarian aspect, which raises the question about how much someone else legally married really impacts others. While I don’t support gay marriage, I do share that feeling. I do think free-willing couples should have the same legal, government rights, but IMO it should not be a marriage, as that is a biblical role. I sort of feel like others here that government needs to get out of the marriage business all together, and just have legal partnerships/civil unions, etc. Then, those married in a church apply for the legal contract, and others can too if they so choose.
If you're in chains and the chains are chafing, seeing someone else's chain cut can provide a psychological boost. That's why prisoners cheer on (and even help) escapees even though they themselves are not one iota freer as a result. If society is overlawed into becoming a kind of prison, you'll see the same attitude in the general public.
Unfortunately, in too many cases, freedom-lungers are reacting emotionally rather than acting rationally.