RAM sticks are designed to comply with JEDEC industrial standard, so in theory (and my decades-old experience backs this), regardless of manufacturer, if they have same parameters, they will work together.
Now, as others pointed out, working together doesn't mean "without issues". That is why, to avoid ANY POTENTIAL PROBLEM, it's always better to invest in RAM kits - which are sticks bundled by the manufacturer, coming from same batch, maybe even with consecutive serial numbers, and tested together (of course) - to eliminate as much compatibility issues as possible.
Some of the issues are, for example, linked to base material. That is: silicone wafers used to manufacture them are coming from same slice and were next to each other, pathways are from same batch of alloy etc. It is not a secret for a long time now, that - for example - faster CPUs usually come from the middle of a silicone wafer, while slower ones from the edge of the wafer.
The point is that, regardless of the technology progress, basic materials still matter when squeezing maximum performance from a computer, but not so much if you run it at default speed.
Back to the topic: if you do not overclock the system, sticks from different manufacturers, and even of different parameters, should not cause problems. System will simply step-down one of them, if needed, to match the slower one. That's it.
But start overclocking and there will be blood. Problems would be, first of all, of stability nature, leading to errors (usually hard memory errors), causing crashes. For example.
Right now my PC is running 128GB RAM, with 4 sticks of 32GB Corsair memory. Initially it was 64GB (2x32 GB), which are - in all likelihood - a manufacturer's genuine RAM kit. But I upgraded several weeks later, and since I was suffering from a hangover, I made a mistake and I bought two more, single sticks of same 32GB memory. They are working flawlessly and at their max (according to few benchmarks I ran), but they are DDR5 not designed to be OC'd. And I knew I will not be OC'ing, nor even XMP'ing them because, at the time I was building my rig, XMP on DDR5 would not work on more than 2 sticks, and I need a lot of RAM.
Which brings me to the last point: sometimes tech is not mature enough to meet all the challenges, and you may try with all your might to avoid issues, but to no avail. So, unfortunately, some people found out the XMP issues on quad-RAM-stick-setup the hard way...
Fun fact for the closing: the little research done in the field of RAM issues - mostly in servers, and best one comes from Google, but still valuable - AND published, shows that if there are EC errors, then for the most part the culprit is the MB, according to this source:
... the study found that error rates were motherboard, not DIMM type
or vendor, dependent. This means that some popular mobos have poor EMI
hygiene. Route a memory trace too close to noisy component or shirk on
grounding layers and instant error problems.
EDIT:
Added screenshot of Hwinfo summary to show the config and confirm it's Dual Channel.