Left/right is too simplistic, I am fairly left on many issues but I think making it so that people don't need to migrate is better than allowing unlimited migration which is not a good long term solution...
This is not weird at all if you ever tried to argue with the Left, making blatantly obvious false statements is their way to bait you into arguing semantics and accept the main narrative. E.g. in this case many went after the semantics of the "far-right" and not on the main claim of "birth rates can never recover".