When water is flowing near fences and fence gates, they act like previous versions of Minecraft. The water is blocked by the fences and fence gates. It should pass through the block with the new 1.13 Water Mechanic. Could affect other "partial" blocks.
The waterlogging system does not allow water to flow into other blocks, to avoid breaking existing devices. You can however place water into those blocks and it will spread out, at least for fences. There are some blocks this does not work for, though, which includes fence gates; that is detailed in MC-125351.