As of the latest snapshot, Minecarts on a rail cannot be nudged with movement keys as they normally can. Likely caused by the riding/passenger changes.
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Also applies with horses. Can the reporter or a mod edit the title and summary to include them too?

Horses are a different issue.
Has it been reported yet?

Yes, a few duplicates too. I'll clean them up later.

I'm here and report that all my minecart network doesn't work correctly anymore, none of them will let me ride to the destination, I got killed once and lost all my items (since I consider this as a testing world and this kind of bug is expected I gave myself all the items back), like the Minecart went into the ground and wouldn't let me back up, I had to disconnect from the server and connect back and I was stuck in the rocks around the track and died.

Does this bug aplies to ALL ridable entities?

THIS IS A SERIOUS ISSUE TO ALL MINECART LOVERS

Still Riding...

Can confirm for 42a

no you can't

Confirmed for 15w43b and 15w43c

Confirmed for 15w44a.

Seems to be fixed in 15w44b

Confirmed forward control starts minecart moving 15w44b.