This is a common question in astrology. It is always stated that there's a smell of infidelity in the air whenever the moon is in Libra. It is either the individual will have two (or more) relationships at the same time or wants to have them, at the least. But are they that way just because the sun and the moon says so? Let us count the ways.
Libras are often misjudged as being unfaithful mostly because of the flirtatious nature they posses. They fall in and out of love at the drop of a hat since they are obsessed with the thought of falling in love. Not that they can't tell what the real thing is from not. They're just not the type who would let something pass if they think there's a tiny bit of a chance that it will work out. As long as they are single and there's a prospect they'd check it out. This may have something to do with their ruling element. Being ruled by the Air element can mean they rarely put depth in relationships they commit to. They can fly away from one relationship top the other. Although they like being in love they also tend to be superficial. They want things that come in the best packaging and whatever is inside can be secondary. They always look for something that will make one leg go up when they kiss, or someone who will sweep them off their feet but most of the times, they worry about how the sweeping will be like more than the person who actually does the sweeping.
One of the traits of the Libra that actually stands out is their being indecisive. This contributes big time to their "unfaithful" image. They would want a lot of options but would be constantly torn between them trying to figure out what their faults are and which one is better. You also have to remember Libras are people pleasers so sometimes it may be hard for them to let go of a person just because they don't want to hurt their feelings. It takes time before they figure out a way to let the person know it's not going to work out between them. They are also friendly which sometimes can be seen as flirting. They wouldn't mind a conversation with anyone as long as it raises their interest.
Again, Libras are commonly misjudged as being unfaithful. Misjudged being the operative word meaning it is not their true nature. They are just misunderstood. Truth be told, among all of the signs, Libras are the least likely to cheat because they are virtuous and fair people. They want to fall head over heels with the right person and they shamelessly search for "the one" that they won't mind checking each one they come across with just incase it's there. They may slip every not and then in their search for the perfect partnership but once they find their true love there's nothing or no one that can make them even think of straying.