I have buddypress installed. Would that be what you mean by "membership plugin"? If so would you recommend I uninstall it? I'm a very basic computer user who had the site designed for me. Can you give me an example of an stmp 3rd party plugin with extended logs? I will install it.

I mean is any other 3rd party plugin manages the new users signup ? Some conflict perhaps ? Hard to guess.

As for the smtp, try this

https://wordpress.org/plugins/post-smtp/

or this

https://wordpress.org/plugins/easy-wp-smtp/

both have extended logs or debug features.

Also if you want/can a url could help so we can test.

No there aren't. The only plugins I have are akismet anti-spam, bloom, buddy press, contact form 7, cookie notice, google analytics dashboard notice for WP, ithemes securit, jetpack by wordpress.com, monarch plugin, the events calender, updraft plus, valvet blues update urls, woocommerce, woocommerce services, wpforo and yoast ceo.

My forum is www.5gawareness.com/forum

I've just installed post SMTP and now on the setup wizard. It's asking me for my sender details so I wrote my admin email for my site. Now it's asking me for my outgoing mail server hostname. Is there a way to find this out?

Well the outgoing (smtp) address depends on the hosting setup. And details are provided when you register a hosting plan. Could be "mail.your domain.com" or locahost or your provider's email smtp. I can't help in that.

Tried to register. I got

"Members not found " message when i clicked Register.

BUT i got the email all right: (from Received: from mail-gw.thundermail.uk ([149.255.60.76]:35960)

Username: test_1 To set your password, visit the following address:

So all work ok. I see no problem in emails.