Well unless you object to the term 'skincare nerd' Nabootique, ehm yes 
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I agree absolutely wrt to The Ordinary, their affordability is a bit of a curse and blessing in one. I think another part of the problem is that The Ordinary is not a traditional range in the sense that you can buy your entire routine there but that's how most will try to understand it. I know there was a dedicated thread on here where the OP gave up after a week of exclusive use of The Ordinary since it didn't seem to do anything and I think that won't be a too uncommon practice in this initial boom period. I don't mean to pick on that poster specifically but it did show the lack of research that comes with those products and how it should fit in with a routine and what reasonable expectations are.
Any products that shouldn't be used together, or benefit from being used one after the other?
The reason why I like Vit C so much is because it's a great support player, it makes both Retinol and SPF more effective alongside its own benefits to the skin.
There is also a general benefit to use your most active products first according to pH level and consistency. Order would be: Cleanser - Vit C - Acids (BHA before AHA if using both) - Serum - Moisturiser - SPF
There's a few popular myths, Vitamin C and Niacinamide can cause flushing and that Vitamin C and Sodium Benzoate (a quite common preservative) form cancerous Benzene.
Now most of these internet myths originate from studies where it does prove this to be the case but it is usually at quite specific conditions to cause these reactions. The thing is we don't always know the concentrations, the conditions, the pH, etc. but anything potentially hazardous (like Retinol during pregnancy) or non compatible (The Ordinary does advice not to use their Vit C and Nia together) would be disclosed by companies to cover themselves legally. So while caution is warranted, especially if you prefer to err on the side of safety (I don't like to mix my current Vit C and anything with S.B. since I'm unsure of the exact concentration of VitC) these tend to be internet gathered knowledge rather than scientific fact.
There is also the myth to wait between your actives (20 mins) to allow your skin to readjust itself pH wise. Which means if you're using Vit C, BHA, and AHA you'd be sitting there waiting an hour before you even get to the serum stage unless you use a pH adjusting toner in between each step. Paula's Choice clearly states on her website that her acids are formulated to be used without waiting time and most manufacturers will tell you the same. I've seen no difference between waiting and not when I foolishly attempted it for a week.
A lot of these myths tend to originate from people getting wrought up in scientific papers online and drawing their own conclusions and applying them haphazardly elsewhere without even a degree in anything scientific. The same can be said for parabens, alcohol in skincare, mineral oil, and to a certain extent silicones.
What else do these things have in common beyond demonisation on the basis of circumstantial evidence? They're used mostly in simpler (ie. affordable) formulations. I will happily discriminate against a £££ product when the second ingredient is mineral oil as it simply can't ever justify its price unless the first ingredient is pure gold or uses parabens as their preservatives when they can clearly afford to spend money on an equally safe preservative with a superior cosmetic elegance.
The biggest problem with demonising these ingredients is that the alternatives used are actually unsafer or more harmful, this is especially the case with parabens. Everyone knows how to look out for them but has no understanding of the alternatives, or even worse the complete lack of preservatives causing people to use contaminated products with terrible repercussions.
The case against alcohol is mainly based on studies pertaining to tissue damage on internal organs. I'm personally not a fan of denatured alcohol (no one seems to discriminate against the fatty alcohols like cetyl, stearyl, and cetearyl) as it can be drying but it has its place in formulations, specifically in sunscreens. It helps penetrate the active ingredients much quicker and more effectively and mostly evaporates during the process.
I don't like the feel of silicones personally, and the fact that it can make your skin feel and look better than it actually is. So while your face doesn't appear to be as dry as it was, the condition isn't actually improving. There's also some environmental consequences that make me question the prolific use somewhat. Dimethicone seems to be the most common and actually least problematic whilst others seem to trigger and some have been disallowed for use in the EU. They are however great stabilisers for formulations and non toxic so have their place. My biggest issue with silicones is that if you use several thin layers of different products with silicones in them, they tend to ball up with all the rubbing, often ruining your makeup and possibly compromising your sunscreen protection in the process. So anything with silicones will be towards the very end or last step of my routine, so usually SPF and makeup.
Fragrance is an annoying one, I can go either way with it but is often irritating. The frustrating thing is that a fragrance is protected and its INCI is not required to be disclosed. A manufacturer can therefore hide a myriad of things including possible irritants in there and make dishonest claims, eg. parabens or alcohol within the fragrance and still claim the product is free of it.
So in short, unless you find one of those 'controversial' ingredients to be clogging, irritating, causing an allergic reaction, etc. there's no need to actively avoid them.