Absolutely it's a sincere belief. "Slave" is hyperbole, but only just barely.
The link you posted indicates that 80% of people think it's reasonable to show ID at a polling station. I think you'd find that's a pretty common opinion on it's face because it's perfectly reasonable to show ID to do things like vote or get social security benefits or register property you own or all those government-y things.
The trouble comes when you hijack that perfectly reasonable expectation by then making ID preferentially difficult to get for certain classes of people. You don't need to trust that this is the case - it's apparent from the statistics. More than 10% of adult US citizens don't have ID. Why not? Because it takes time and money - you need to pay fees, you need to travel, you need underlying documents that can sometimes take hundreds of dollars of fees themselves to generate, etc. Politicians also can 'tune' what counts as ID to preselect the voters they want. TX for example, counts concealed carry cards as ID but does not count student IDs.
In fact, in 2014 the GAO itself found that strict photo ID laws reduce turnout by at least 2-3 percentage points on average with significantly higher proportions in economically depressed and racially diverse areas, and it's well documented that the people impacted by that lower turnout are overwhelmingly members of specific demographics that tend to vote for specific policies. That's a pretty big incentive to marginalize these people if you don't agree with those policies.
It's undeniable that for many of the most vulnerable and powerless members of society obtaining ID under the current regime is in direct conflict with simple survival, and is unlikely to be a priority. If we want to require ID for voting we should make the process of obtaining that ID require as little economic power as possible - a task that is easily within our grasp.