This is based on this issue - https://bugs.mojang.com/browse/MC-131058

I decided to make a new bug report just to make it more clear.

From my initial test, I noticed that water wasn't flowing over signs, but did flow over fence gates.

Testing some blocks where water doesn't flow over it -

Slabs - bottom half only. Top half slabs work.
Signs - Placed on the ground and against another block.
Trapdoors - Open and closed.
Chests - Trapped Chests, normal chests and enderchest.
Ladders
Sea Pickle - Up to the max number of sea pickles.
Fences
Iron Bars

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From the above, I am seeing a pattern - any block that can be waterlogged - has the waterlogged tag (but, water will not flow over it. If the block can not be waterlogged, then water flows over it as expected. Water will flow if the below waterlogged block has the waterlogged tag set to true.

In the below example, the bottom iron fence is a block that has the waterlogged tag, but it is false as there is no water flowing from it. The water on top will not flow. 

The iron fence on the top is waterlogged and does flow. When I placed a water source block on top, the water on top also flowed.