How to disable horizontal scrolling
I've written a solution that disables horizontal scrolling, (by riffing off of @ЯрославРахматуллин's suggestion), but I don't think you're going to like it:
autocmd CursorMoved * norm!99zH
This prevents scrolling to the right by the incredibly precise method of just scrolling back again.*
* Because I don't know how far you've scrolled to the right or how long your lines are, I'm scrolling the arbitrarily "far" amount of 99 half screen widths. Note also that I'm not bothering to check whether or not you've actually scrolled to the right before scrolling "back" to the left. If you actually intend to use this solution you might want to knock something up by comparing the values of
Why you're not going to want to do so
The reason that you're not going to use this is that underlying the scrolling problem is another issue: Vim won't let you move the cursor "off screen". Therefore, if you scroll to the left in a way such that the cursor would be off screen after the scroll, Vim helpfully brings the cursor along with it and moves it to the left.
But because the calculation it's using for whether the cursor is on screen is the same as the one it's using for deciding whether to scroll in the original problem, the net effect is that with this "solution" in place, if you attempt to move the cursor to the right in a situation that would normally cause a sideways scroll, now the cursor refuses to move at all.**
**To be slightly more precise, depending on the current position and the movement, the cursor may move rightwards; it just won't move past the position where a scroll would normally occur.
So I'm afraid your planned workaround isn't going to pan out. If you want a workable solution to the general problem, it's going to need to be implemented in the Vim source code.
As you've already noted, this is unlikely to arrive any time soon, so I'm afraid your best bet for a workaround to the specific instance of the issue shown in your gif is to petition the plugin author to stop using
conceal entirely and instead remove the hidden text from the buffer entirely.
Based on the unconcealed output and the mention of
vim-plugin-AnsiEsc in the documentation this might be something it's possible for them to implement, but it's hard to say for sure without knowledge of how the plugin functions.