As you can see the water is flowing perfectly fine in both directions for other splits. There is very little flow through these pipes, so it's not a lack of water. As a result of this apparent blockage my toilets aren't functional.
Each segment of pipe only flows in a specific direction, and can only ever flow in that direction. Even if the pipe segment is empty it still blocks liquid entering it against that preferred direction, and liquid can't flow out of it against that preferred direction even if the preferred direction is blocked. This is not how pipes work in the real world, it's a "gamified" model used to make the behaviour simpler (both so that it takes less CPU crunching to calculate it, and so that human players can make predictions based on hard and simple rules, instead of messy real-world physics).
As you build a pipe network the game has to assign a direction to every bit of pipe, updating it as you reconfigure the network. But for some networks there isn't an unambiguous "correct" way to do this, so the game has to just do it arbitrarily1.
Take a look at this terrible drawing of a quite simple pipe network:
From this, the game has to decide which direction each stretch of pipe should flow. It can use the positions of sources (places where fluid enters the pipe network; these are output ports of buildings that connect to pipes) and sinks (places where fluid leaves the pipe network; input ports on buildings) to tell which direction most of these pipes must flow. This is because it always has to flow away from sources (like pumps) and towards sinks (like vents or buildings with a pipe input).
However that horizontal section of pipe is an issue. Should it flow like this:
Or like this:
Either direction has the fluid splitting on one side, flowing across to the other side, and then merging there. Both ways "work", so how should the game decide? You probably had a way you wanted it to flow in mind when you built it, but the game doesn't know that. So it will have to arbitrarily pick left or right. Sometimes it will simply pick a direction that is different from your intent.
So back to the original question. In this case you haven't shown any of the network to the right, but I actually don't need to see it to say what's going on. If a pipe is flowing a different direction than you wanted it always comes down to a (more complex version of) the situation I have described here.
If you only had sinks to the right, then flow would have to go to the right as you desire. But there must be a source somewhere reachable by following that pipe (perhaps it's simply the output side of your toilets), and the game has obviously decided that liquid should flow from that source and along this pipe to the left, merging into the flow going to the electrolyser. It doesn't matter that there isn't actually any liquid right now to flow in that direction; whether or not there is any liquid in the pipes (and whether it's moving or blocked) the game knows for each pipe which direction liquid should flow along it, and that's the only way liquid can flow. It only changes if you change something about the pipe network; in particular a connection like this will not work to balance out two pipe networks where liquid would need to flow one way or the other depending on which side has excess liquid available.
There is fortunately a simple way to fix it (if you only want it to flow in one direction but the game has picked the wrong one); use a bridge (or a valve, or even a tank - anything that takes in liquid and immediately outputs it again) to break up the pipe that is flowing the "wrong" way.
Now there aren't multiple valid solutions for which direction the pipe should flow any more, there's only a single one that works: the one that you wanted.
In your example, simply break up the pipe leading to the right of the screen with a bridge. From the point of view of this part of the pipe network, you replace the entire complicated network off screen to the right with a single fluid sink. At the junction with the electrolyser, the branch leading to the right would now go towards the input side of the bridge, so the game obviously cannot assign that segment of pipe flowing left, and so the electrolyser junction has to be splitting flow between the electrolyser and the bridge, instead of trying to merge flow from the left and right in to the electrolyser.
1 I assume that the "arbitrary" way the game decides ambiguous cases isn't actually completely arbitrary. If you know more about how the game works you can probably predict it. But it's arbitrary in that it doesn't follow just from the layout of the pipe network. Rather than memorizing whatever criteria the game does use and trying to manipulate them to get these sort of pipes flowing in a chosen direction, I prefer to just treat them as "unknowable" and put in my own bridges to make sure the network works the way I want it to. This also makes it more stable (less prone to suddenly breaking when I add something to the pipes that I thought was unrelated).