There was an Ask Lemmy post about descaler and it reminded me of an experience from my own household adventures.
I use both Iron Out and Barkeepers Friend at home to deal with my foundation drains. Both products have different formulas with different mechanisms and they are not compatible. I'm thankful I am so paranoid or else I might not have realized and potentially created a harmful situation in my basement (a particularly bad place for the heavy gas that forms!).
Iron Out
Liquid forms are called Super Iron Out and Super Iron Out Outdoors.


Both have oxalic acid as the active ingredients although the SDS for Super Iron Out says Oxalic acid and the Iron Out Outdoors says Ethanedioic acid, dihydrate.

Both Oxalic acid and Ethanedioic acid, dihydrate are powders, not solutions. On the surface this probably seems extremely autistic of me and it is, but it's also really important.
Let's look at the CAS number given on the SDS. Oxalic Acid is given CAS 144-62-7 Ethanedioic acid, dihydrate is given 6153-56-6. Ethanedioic acid is another name for Oxalic acid and the reason for the different CAS number is the "dihydrate". This distinction only matters in solid form. If it's in a solution it's the same damn thing (except for the fact that it ionizes into two forms and the relative abundance of each depends on pH). Therefore it is needlessly confusing and wrong and I hate that lol. That's not the point of the post but I needed to get that out.
The solid form of Iron Out is a mixture of different compounds, none of which are any powdered version of Oxalic acid.

It contains Sodium hydrosulfite, Sodium metabisulfite, Sodium sulfite, Sodium Carbonate and Citric acid. It's super tempting to break these out into what they do but they can perform multiple roles and that will come up later.
Barkeeper's Friend
Barkeepers Friend also has solid and liquid versions.
The solid version is called Cleaner and Polish or Cookware.


The active ingredients are Oxalic Acid (CAS #144-62-7), a surfactant and an abrasive. The difference in the two formulas are the surfactant and abrasive, but neither of these are involved in why the two formulas are not compatible so I'll gloss over that.
The liquid versions are called Soft or Multipurpose.


They still use oxalic acid as the main ingredient but again different quantities (or no) abrasives and different surfactants.
What's your point?
You should not mix Oxalic acid and sulfites. Sulfides can react with acids (even weak ones) and form hydrogen sulfide gas. I have more experience with SO2 than I want and I can give you my professional option that it fucking sucks.
So if you are not careful and assume Iron Out and Barkeepers friend are interchangable you may have a bad time. Or, if you are using them for different purposes (powder iron out to remove iron deposits and oxalic acid to control biofilm growth) you may also have a bad time.
Don't they do the same thing? Why are they not compatible?
Kinda but not really.
Rust is stupid complicated actually. It's often simplified as Iron(III) Oxide but that's absolutely not the whole story even though it sounds super technical. It's useful because if the three oxidation states of iron this is the one that flakes off most easily.
There are probably multiple reasons but intended use of both products is likely why the formulas are different.
Barkeepers friend is primarily used on metal surfaces which might have corrosion and to remove the resultant rust. The reaction between oxalic acid and rust isn't one step and it isn't simple because both the iron oxide and the oxalic acid exist in different states in solution, largely dependent on pH.
I think the easiest way to explain is to contrast with Muriatic acid (HCl). HCl is a strong acid (It's got an estimated pKa of -5.9) and will brute force the insoluble iron oxide apart and form a soluble Iron chloride. The iron oxide is acting as the base in the acid-base reaction. If the acid then goes on to contact more iron in the metal it will oxidize it so that the formation of oxides will occur more readily. So it can remove rust and encourage new rust. Neat.
Oxalic acid is a weak acid. The two forms have pKa of 1.2 and 4.2. Oxalic acid is not doing an acid-base reaction with the oxides. It reacts with Iron(III) oxides to form a soluble complex. This is called chelation. It's more complicated than that of course but what is important to remember is that it is reductive not oxidative. It's not absolutely safe for stainless steel but it's way less aggressive than Muriatic acid.
Iron Out on the other hand is more focused on removing iron deposits on non metallic surfaces. The combo of sodium hydrosulfite and sodium metabisulfite was patented by Hach as a rust remover from non metallic surfaces. They are stable powders that when made into solution form soluble iron sulfite from iron oxide via reduction.
Citric acid and sodium carbonate also work together. Sodium carbonate raises the pH of the solution so the citrates can still do chelation without the level of attacks on metal metal what would occur at lower pH.
Sodium sulfite is probably there as an oxygen scavenger and corrosion inhibitor so that any oxidized iron that exists does not as easily form an oxide. Again this is likely related to the use of both products as iron out powder isn't always rinsed off right away like barkeepers friend is.
So while Iron Out also considers risk to metallic surfaces, the cleating agents likely selected knowing use on metal is not the main intent. Cost is probably also a factor.
TL;DR:
Maybe just don't mix cleaning chemicals ever. Even if they have the same "purpose" or even the same name they might use different, incompatible active ingredients.