Sound quality can be divided into amplitude, timbre and pitch. If there’s an impedance mismatch between your two devices connected to the single output, you could have a large mismatch between the levels arriving at each device. If the difference is large enough, one device may have distorted or inaudible audio.
To avoid this, you should ensure that both devices connected to the split signal are similar - such as 2 pairs of headphones, 2 recorder inputs, and so on. When you place 2 devices with wildly differing load impedances on a splitter is when you’ll encounter problems - such as headphones on one split and a guitar amp input on the other.
To get around this, you can use either a distribution amplifier (D.A.) or a transformer balanced/isolated splitter - which will work over a larger range of load impedances, typically. Depends on the quality of the splitter and the exact signal path. If you’re using the splitter to hook two things into one input, and you’re using quality connectors, you probably won’t lose much quality. There can be an increase in impedance of the cable due to the imperfect continuity of the physical connection, however with unbalanced line-level signals, impedance at both ends of the chain tends to be orders of magnitude higher than the connection will create, so one split will be barely noticeable. So too, the noise increase from the additional length of cable.
Now, one source into two inputs, that will by basic math and physics result in a 3dB drop in signal strength, which will reduce SNR by about that much. By splitting the signal path between two inputs of equal impedance, half of the wattage is being consumed by one input and half by the other (the equation changes if the inputs have significantly different impedances). So each input gets half the wattage produced by the source to drive the signal on the input cable, and in decibel terms a halving of power is a 3dB reduction. Significant, until you just turn the gain back up. The “noise floor” will be raised by however much noise is inherent in the signal path between the split and the output of the gain stage; for pro audio this is usually infinitesimal, but consumer audio can have some really noisy electronics, both for lower cost and because you’re not expected to be “re-amping” signals several times between the source and output.
