Different amplifier or pedal input stages may have different characteristics. The sound of a guitar will be affected in some measure by the characteristics of the device to which it is connected. To use a mechanical analogy, consider the relationship between the strings and the sounding board on an acoustic guitar. The strings try to move the sounding board, but the sounding board in turn pushes back on the strings. The way in which the strings and sounding board actually move depends in a complex way on the interaction between them.
Many kinds of amplifier input stages are deliberately designed to behave as much as possible like "passive observers" [called a "high-impedance input"], and many amplifier output stages are designed to behave as much as possible like rigid motion controls [a "low-impedance output"]. If the string vibrates by 0.1", then a passive amplifier which was set for a 2:1 gain would not affect the vibration of the string, but would cause anything to which its output was attached to vibrate by 0.2", regardless of how much or how little force was required to do that.
Adding a buffer stage between two devices will make it impossible for the latter device to affect the signal coming from the former. In many cases, amplifiers are deliberately designed to minimize the effect that downstream devices have on upstream ones, so the fact that any residual effect (which isn't supposed to exist) doesn't get transmitted is not a problem. Because the direct signal from a guitar is not driven very strongly, it will often thus be liable to pick up noise. The signal from a buffered bypass may convey the same amount of "motion", but will be driven as strongly as necessary to produce that motion, making it less liable to pick up noise.
Although many amplifiers and pedals are designed to have only minimal effect on the incoming signal, that isn't true of all of them. Imagine, for example, a pedal which was wired just like the tone control on a guitar [e.g. to add a "tone control" function to a guitar which would otherwise lack one]. The tone control circuit sits across the guitar coil's output, and is designed to be electrically "move" easily at low frequencies, but with greater difficulty at higher frequencies. If a guitar were plugged directly into a pedal containing a similar circuit, or if it were plugged in through a pedal with a "true bypass", the tone control would work the same way as on a guitar. If, however, it were plugged in through a pedal with a "buffered bypass", the tone control would have very little effect since a typical buffered bypass is designed to overpower any "stiffness" the downstream device might have.
If an amplifier's input stage would affect the signal that gets fed into it, then such behavior will be totally changed by the addition of a buffered bypass. If such effects were desirable, the lack of them would be a bad thing. If such effects occurred but were considered undesirable, the lack of them could be a good thing. Only if the input stages of the buffered bypass matches that of the downstream recipient of the signal will there be no effect; effects when they occur, however, may be either good or bad. Unless one is deliberately using an amplifier or effects pedal which is designed to affect its input, however, the only way to know whether a change will be good or bad is to try it.