You're right to call them on out this, as it's been an absurd claim from conservatives for several decades now. These days, they hate individual choice whenever that might threaten the interests of wealthy white men; trans rights, voting rights, abortion, etc.

That said, they have been ideologically consistent on this when it suits their needs: guns, schools, healthcare, the environment. It's a selfish stance that results in terrible, destructive policy on all of those issues, but in those areas "individual choice" is still a genuine conservative ideal.