Rosalyn

Sadly this isn’t a secure solution that we can rely on to prevent anyone joining. We need Squarespace to act.
As Michael explains, this cannot prevent users from joining your Member Area because it isn’t preventing the account creation process from working - it is simply hiding the link from those who don’t know how to find it. Anyone could still join your Member Area, so you’ll want to ensure that you aren’t sharing anything private or valuable. 

I need this feature as well. I just paid for and published a private member area that I later learned anyone can become a member of.
For squarespace: While I'm grateful for the release, being clear about these constraints would have been helpful, warranted even. A "member area" implies privacy or exclusivity, if it's not it's just another space. So I'd recommend prioritizing the product roadmap to address this immediately or rename the feature to "Subscription area".

This is so wildly frustrating. I'm so amazed at the messiness of this and 7.1. I've just discovered I can't edit the password protected pages either, so trying to work around the bonkers Members limitations with password protected pages in 7.1 is an ugly adventure into the laziness of Squarespace.

Holy crap that's worrying. Really sorry to hear that!

It didn't seem appropriate to 'like' your post, but I do sympathise. It's a stark reminder, if one were needed. I hope that others realise this before they use any membership products.