Filtering on any signal outputs, and probably ESD protection, is an absolute minimum. An MCU pin toggling regularly has harmonics up into the 100s of MHz. An LC lowpass made from a ferrite bead (30 to 1000 ohms at 100MHz, depending), and a C0G say 100 to 1000pF, is a good start. Clamp diodes for ESD are also a good idea.
Just ferrite beads might well address the linked question, or at least afford considerable reduction.
If the LEDs themselves produce noise (what are they, PWM once set? I forget), there's not much you can do about that. Preferably they would be made on a two-layer strip (one side ground plane), with frequent supply bypass capacitors, but if they're just parallel traces on a single layer, you're a bit screwed, short of a mesh screen over the whole damn thing.
Tim