I'm not familiar with these debates, but I can assure you that you are absolutely right to say SLIDERS was shot on film: 35mm film in Seasons 1 - 3 and 16mm film in Season 4 - 5. You don't need to 'believe' it, you're correct and it's an objective fact.
If anyone ever told you it wasn't shot on film, they are confused and mistaken. I can right away that it is film from the film grain.
When film is exposed to light, silver halide crystals in the film experience a chemical reaction with tiny particles of metallic silver which create the visible image and creates the texture of grain. This grain is clearly present in the Pilot and Seasons 2 - 3, and the grains get comparatively larger in Seasons 4 - 5, and it's very recognizably 16mm film.
Videotape does not have film grain because it records a purely electronic signal without the chemical reactions for grain.
(Most modern TV and film is shot with digital cameras, and in most cases, film grain is added afterwards to mimic the texture of chemical film, and it adds a bit of texture while being less perceptible because it's uniform and consistent as opposed to variable to the image content. And on streaming, digital files are encoded to smooth out most of the grain (reducing file size) and uniform grain is overlaid during playback.)
Grain is not as visible on episodes 102 - 109 due to the episodes having been stored on low resolution analog videotape that didn't maintain even an SD version of the original film and its grainy properties. However, 102 to 109 were also clearly shot on film: while they lack visible film grain, they have all the signs of film-to-tape conversion.
They have judder -- uneven motion -- in fast moving scenes. They also have interlacing artifacts: horizontal lines during motion and jagged edges on straight lines like chains, fences, poles and shelves. This is the result of the film to tape telecine process where the 24fps frame rate format of film was converted to the TV broadcast 30fps videotape.
Videotape would not have judder or interlacing artifacts; those are exclusively the result of film to tape telecine conversion.
Also, videotape has a very flat colour range and the dynamic range of SLIDERS, even in those beige rooms of Seasons 4 - 5, is beyond what videotape could record.
If there were ever any debate about whether or not SLIDERS was shot on film, it was likely due to people being misinformed about and/or misunderstanding TV editing. The pilot was shot and edited on film as a big budget TV movie to sell a subsequent series, and then it was transferred to high grade videotape with 420 lines of resolution, used for review and sales and broadcast. However, the following episodes of the show were shot on film and then transferred to videotape for post production.
Unlike film, videotape offered linear editing, immediate playback, and needed no chemical processing, providing a faster turnaround time essential for TV production. The show seems to have used standard but low resolution analog videotape format for episodes 102 to 109 which is why those episodes are blurrier.
Low resolution videotape was cheaper and, for standard definition 480i broadcast and CRT viewing, the viewer couldn't tell that it was blurrier, so it didn't matter. Only when the DVDs were played on a mid-2000s HDTV did the poor video quality become apparent.
In Season 2, there was clearly a switch to high resolution digital videotape, meaning we go from "Luck of the Draw"'s fuzziness to "Into the Mystic" looking sharper with another increase in sharpness for Season 3 and a slightly more grainy look for Seasons 4 - 5. Digital videotape with 540 lines of resolution became the affordable industry standard during the long production gap between "Luck of the Draw" and "Into The Mystic", with improvement each year in the film to digital tape telecine process.
If fans were ever debating whether or not SLIDERS was film or videotape, it's likely because SLIDERS was shot on film and, aside from the pilot, transferred to videotape for editing and special effects, and stored on videotape for broadcast and later digitized from videotape to DVD. Fans were likely confused by production references to videotape suites for editing and effects. In addition, there were isolated B-roll sequences (sports footage, etc,) that were recorded on videotape, but it's maybe 2 percent of the show.
SLIDERS on DVD has film grain and all the artifacts of a film to tape conversion: judder and interlacing artifacts. If shot on videotape, there would be neither grain nor judder nor artifacts. You don't need to believe you're right about this matter; you're making a statement of fact and you are correct.