The Full Moon doesn’t just signify conflict in the birth chart, and the reason you think it does is because you misunderstand the lot of fortune.
The lot of fortune is based on the space between the sun and moon. A Full Moon means the sun and moon are?around 6 houses apart. In whole sign houses, the lot of fortune likely lands in the 7th house.
Modern astrologers claim the Lot of Fortune is about luck, but that has no basis in its actual purpose. It tells you what you’ll receive in life, good or bad. Fortune in astrology is more about fate than luck. If it's in an angular house, like the 7th, that supercharges it. A LoF in the 2nd may center on gaining and losing wealth; in the 7th, it focuses on gaining and losing actual people. So most Full Moon natives feel caught in fated relationships, partnerships, and friendships, with lives centered on who's around them at any time.
If the Lot’s ruler is well-placed, interactions are good. If badly placed, conflict is likely.
The conflict idea stems from the sun and moon. The sun represents the father; the moon, the mother. When opposed, it might indicate parental conflict. But that's not the full story. If well-placed or received, it can just mean the parents occupy different life spaces. Sun in the 4th and moon in the 10th—the native links the mother with prominence and career, the father with home and lineage. Opposed yet positively connected.
Another case: sun in the 9th, moon in the 3rd, with the MC/IC line there. Both parents might have taught spirituality from different angles. Here, both are in their joys, so conflict is far less likely.