Why do they even bother? This is going to hit the front page of every health/fitness/cycling/running blog site, there will be a big stink for a few weeks, then Withings will quietly (or loudly, "we've heard you!", as if they were listening in the first place) get rid of it. And they'll waste all this time, money, and customer goodwill for nothing, because no one could have possibly seen this backlash coming.
Doesn't matter to me, neither their POS blood pressure cuff nor their scale will sync to HealthKit anyway (oh, how I've tried), I'm not losing anything. So stomping my feet with "I'm never buying another Withings product!" won't make any difference, I was not going to buy their POS products again anyway. :-)
Will they get rid of it? It seems more likely that they'll do damage control to wait out the news cycle (the official comment on the linked post is an excellent example of corporate deflection) and change nothing.
I used to have issues with my Withings scale not syncing to HealthKit, but I just checked and it had all of my weightings in there just fine. Can't even remember the last time I checked the Withings app.
This change sucks (but as a long time Withings user doesn't affect me... for now), but I haven't had trouble with either the scale or BP cuff syncing to Apple Health. I don't have any suggestions besides double-checking the Withings app has permissions to write to HealthKit. I don't see any settings in the Withings app itself besides a prompt to check "Settings > Privacy > Health > Withings App".
Sorry if this isn't helpful.
Aside: all BP cuffs and their apps sorta seem to suck when it comes to sync. I also have an Omron. At least mine measure accurately. Make sure to validate yours with your GP.