I only see this argument made by conservatives. It is a deliberate attempt to drive a racist and LGBT-phobic wedge between the white working class and the Democratic Party. I have never seen a progressive person demand less support for the rights of minorities.
I also favor raising the minimum wage, making universities free to attend, and having universal healthcare - but LGBT rights aren’t the reason we don’t have those things. The GOP is the reason we don’t have those things, and it’s not like if the Dems said “Fuck it, arrest and kill the gays” that the GOP would suddenly support workers’ rights.
If you want to help the poor, vote out the party that says shit like this.