Nope, you can just click skip. If the device had previously been enrolled in Find My iPhone you have to log back in to turn it off, but if it’s fresh out of the box you don’t have to hook it to iCloud/iTunes at all (and that’s not uncommon to block in corporate environments).

Not on my end, no skip button.

Not sure what device you’re on but every iphone I’ve set up I’ve (at least initially) skipped signing in. It’s not hidden or subtle or anything (especially compared to latest windows OS), it’s a big Skip link. The main downside is you can’t install any apps, and in my experience iMessage does NOT work until you log in with apple ID, just SMS/MMS.

Could be country specific..

True, or carrier lock specific if it involves activation. I would be surprised by this though, and deeply dislike the idea.

Phone still works without an ID. No idea if this means that you can only send SMS messages though.

I’m not logged in I can send iMessages and FaceTime, seems to link it to the phone number though.

It does.