> Jews are an ethnoreligious group, not a religion
This is presenting the two categories as mutually exclusive, when they aren't.
Another commonly cited example of an ethnoreligious group are the Druze–which are even more closed than Judaism is, they haven't accepted converts since the 11th century; Jews disagree among themselves as to what conversions are valid, but the Druze answer is very simple – none are, unless they happened (almost) a thousand years ago. But the fact that Druze are an ethnoreligious group, doesn't mean they aren't a religion – they are. Of course, many Druze nowadays don't take their religion that seriously (the same is true of many Catholics and Muslims and Buddhists), but that doesn't mean the Druze religion doesn't have identifiable theological content (e.g. the Epistles of Wisdom) which make it a religion.
In the UK, Sikhs are legally classified as an "ethnoreligious group" (see Mandla v Dowell-Lee [1982] UKHL 7), but that doesn't mean Sikhism isn't a religion. Again, Sikhism has clearly identifiable religious teachings (e.g. the Guru Granth Sahib). Sikhism isn't hard to convert to at all, but that wasn't seen as relevant by the UK legal system; while it (mostly) doesn't actively evangelise like many Christians or Muslims do, it doesn't try to filter potential converts for their seriousness like Judaism does. The low level of conversion to Sikhism seems to be more due to few non-Sikhs being interested in it, rather than Sikhs trying to discourage non-Sikhs from doing so.
> you can be Jewish and atheist
You can also be Christian and an atheist. See https://en.wikipedia.org/wiki/Christian_atheism
To quote leading New Atheist Richard Dawkins, "I call myself a cultural Christian"
Of course, "Jewish as a non-religious identity" and "Christian as a non-religious identity" don't work in completely the same way – but they don't work in completely different ways either. And consider Northern Ireland, where asking an atheist whether they are a Catholic atheist or a Protestant atheist or neither makes much more sense than it would in most of the rest of the world.
