One thing is for sure, I do not live in your bubble nor would I want to.
No, your projection doesn't work.
Here is what happens when you don't live in a bubble and don't have confirmation bias. You read an article providing proof that Obama lied about his support for traditional marriage:
Obama backed same-sex marriage in 1996By BEN SMITH 01/13/2009
A document has emerged suggesting that Obama had taken more public, liberal stands in the past than had been revealed in the digging of reporters and opposition researchers over two years of campaigning, the latest of several pointing to a rightward shift as he moved into national politics.
In a 1996 questionnaire filled out for a Chicago gay and lesbian newspaper, then called Outlines, Obama came out clearly in favor of same-sex marriage, which he has opposed on the public record throughout his short career in national politics.
“I favor legalizing same-sex marriages,and would fight efforts to prohibit such marriages,” Obama wrote in the typed, signed, statement.
There was no use of “civil unions,” and "no compromise whatsoever," the Windy City Times story today notes.
On another questionnaire the same year, Obama said he would support a resolution in support of same-sex marriage.
The editor of the Windy City Times, a successor of Outlines, Tracy Baim, said she hadn't deliberately held onto the news until after Obama's election. Baim, who had been the editor of Outlines at the time, said that just before the election, she ran across the old Outline story saying Obama backed same-sex marriage, but only dug his forgotten questionaire out of an old box this week, having assumed that she'd lost it.
Obama now says he opposes same-sex marriage, though he backs giving gays and lesbians a parallel package of marriage-like rights, and opposes a federal ban on same-sex marriage.
https://www.politico.com/blogs/ben-smith/2009/01/obama-backed-same-sex-marriage-in-1996-015306And proof that Obama's gay marriage epiphany was the result of pressure from his large gay donors:
There was, of course, cold politics behind it. One in six of Obama's fundraising bundlers is gay, and he needs their money. Wall Street has not backed him financially this year the way it did in 2008. A few Jewish donors have held back over Israel. And when Obama announced recently that he would not issue an executive order barring antigay discrimination for federal contractors, the gay donors all but threatened to leave him high and dry. The unity and intensity of the gay power brokers—absent in the defensive crouch of the Clinton years—proved that FDR's maxim still applied: "I agree with you, I want to do it, now make me do it."Andrew Sullivan on Barack Obama's Gay Marriage EvolutionPublished May 13, 2012
https://www.newsweek.com/andrew-sullivan-barack-obamas-gay-marriage-evolution-65067Step outside your bubble so you can become a more informed citizen.