MOON ASPECT URANUS IN SYNASTRY. GENERAL
The Moon represents our habitual patterns. It is our emotions and can also symbolize the home and family we grew up in. Where the Moon is placed we are searching for emotional security, familiarity, safety and comfort.
Uranus on the other hand is somewhat the opposite. It represents sudden change, excitement, sudden revelation, emotional detachment. Because it is the higher octave of Mercury, it also governs intellectual ideas. Uranus is a generational planet. If you are dating someone within a 3 year gap, and you have a Uranus Moon aspect with them, they also have Uranus Moon in their natal.
When the Moon comes in contact with Uranus we see how these two parts of two people flow or clash with each other. Adding to the sensitivity of this feminine luminary is the fact that the Moon is more personal than Uranus which is generational. That being said, indifferent of the aspect (easy/ difficult), the understanding between these two will depend on the Moon person's Moon. If the Moon person is highly Uranian (any aspect to Uranus, Moon in the 11th house, Moon in Aquarius) she will understand where the Uranus person is coming from, but if this is a water or earth Moon, these people will have a hard time getting one another.
For example I have Uranus trine Moon with a friend. I am the Uranus person and he is the Moon. But he has Uranus trine Moon in his natal and I also have Moon inconjunct Uranus in my natal. He moves home very often because of work and he likes that he doesn't put roots anywhere, and because I also did that in the past (6 times) I kind of get the psychological perspective of it all. Although, distance has been a problem, we have remained friends for 6 years now. But why? My Saturn is forming a trine to his natal Moon (this is new to him he doesn't have it in his natal) and his Saturn conjunct my North Node opposes my Moon by sign (also new stabilizing energy for me). What am I getting at with this? You have to have some stabilizing aspects to Saturn to maintain long-term relationships with Moon Uranus people
MOON CONJUNCT URANUS IN SYNASTRY
The emotional world, day to day reactions and habitual patterns of one person is meeting up with a part of the other that is weird and unusual. The Moon has a sense of familiarity and safety when the other person is acting unique and out of the ordinary. The Moon person can nurture the ingenious part of the Uranus person, and can encourage them to be more progressive. The Uranus person brings excitement into the life of the Moon person, especially in the domestic and emotional sphere. The Uranus person can help the Moon intellectualize its emotions. There is an effect of cooling down the emotions of the Moon.
The Moon is a personal luminary while Uranus is generational. As I was saying in the General portion, the real compatibility between these two celestial bodies depends not on the aspect, but on the placement of the Moon person's Moon. If this is an Aquarius/ 11th house Moon, or if it has Uranus aspects, then this synastry can work out as mentioned above. But if, lets say the Moon is in water and receiving an aspect from Saturn, the Uranus person may be perceived as a "mad scientist" by the Moon individual, bringing intellectual chaos to its emotional stability. This can also bring emotional trauma to the Moon person, especially if the Uranus person sparks feelings in the Moon, and then suddenly disappears, or if its rational responses cannot cater to the Moon's emotional needs.
The Moon is going to experience this synastry in a lesser or wider degree with a whole generation of people. Other contacts between personal planets are needed in order to define this interaction.