I know using a different adapter than the original one can cause problems later on, but is that the same for charging (USB) cables?
This guy here says it's fine
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It's perfectly fine as long as the cable supports charging and not data only
For help on choosing non OEM cable see my answer here How to choose micro USB cable for my device?
My wife has the same device and it works perfectly fine with cable recommended above (or any other cable that supports charging)
Edit: If you are wondering if they support turbo charging - yes they do. Verified on my previous device Moto X Play and my wife's G5plus. Search for cables that support fast charging as they are usually thicker and more efficient
You can use any kind of good data cables (good means original ones made by a registered manufacturer), but make sure those cables are not bought by roadside vendors or a product of local Chinese manufacturer. As Chinese data cables are very low rate of data transfer and they really don't prevent from shocks or electrical glitch, that can seriously damage your phone.
You can also use different Adapters for charging your phone, but make sure that the Input and Output parameters (mA or Amp) are same as yours. As phones are made for specific Input Amps.