The Moon is moving away from the Earth at a rate of 38.08 ± 0.04 mm/year. This is caused by the tidal bulges being pushed ahead of the Moon as the Earth rotates and the landmasses interact with the bulges, pushing them ahead of the Moon. The gravitational interaction between the bulges and the Moon cause the Moon to move faster in its orbit than it should to remain in the same orbit, it moves away from the Earth as a result of this.
Now, sea level rise will affect the interaction of the tidal bulges with the coast lines. But it's not clear to me if the bulges will be pushed more ahead of the Moon causing the Moon to move away from the Earth at a faster rate or if the opposite will happen.