I have a post on the forums about it too
http://www.minecraftforum.net/forums/minecraft-java-edition/recent-updates-and-snapshots/2872793-17w46a-issues-with-tp

The way it worked in 1.12.2, if you were teleporting yourself to your current positon, it would pretty much ignore any axis containing ~ allowing the possibility of commands that can force a player to move in a certain direction but also allow them to move other directions on their own.

In these new snapshots, I can't. If I had

/execute as @a at @s run tp @s ~ ~-0.1 ~

It would push me down slowly, but also I wouldn't be able to move or look anywhere without it rubberbanding back unlike in 1.12.2 where the player would still be able to move on the x and z planes, but would just be sinking down slowly.

I am really hoping that this is a bug or at least will be changed because this broke two of my builds, and I am sure that there are many more players' builds that have also been broken.
And any workaround for this will be very difficult, if not impossible.