Here is sort of my canned response. Email is tough for many people to get right, understandably so, since there can be a lot of complexities and parts that can cause it to be hit or miss.
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Your email settings are probably not configured, or probably mis-configured in some way.
Start here: https://docs.moodle.org/30/en/Messaging_settings
and perhaps take a look at my post here:
https://moodle.org/mod/forum/discuss.php?d=326971#p1315046
You might get your best help by consulting with your hosting provider, if you have one, to figure out your best options for sending email from your Moodle site. Most hosting providers should likely have an email solution for you to use in your email message outputs in Moodle.
++++The specific part of the error that catches my eye, is: "Sender prohibited by SPF"
This would appear to me that your Moodle site is trying to send email FROM an email address, which has a domain, that is not permitted (per SPF policy) to send email from your Moodle site's IP address.
If you don't have any privacy issues with sharing this information, you could show us what you are using in your email server settings:
site admin/plugins/message outputs/email
I would be interested in what settings are being used there, including the "always use no-reply" setting.
Also, particularly, with new user registrations, it is helpful to know what your settings are for:
Moodle may be trying to send email from one of those email addresses configured there. If nothing is configured there, Moodle might be trying to send from the main site admin email address. Bottom line, is that the email address use for what email Moodle is sending FROM must be permitted in some way to be allowed to send email from your Moodle's IP.Also, what Emma said, your hosting provider may be your best resource.
Jamie