There must be an issue with your setup somewhere, because Mailbaby doesn't need to see quotation marks in the SPF record.
The setup that works for me, which is based on a post from here is the following:
In the DNS zone templating (settings/platform), put the SPF record:
type: TXT
Hostname: @
Value: v=spf1 include:spf.hostingcompany.com ~all
TTL: whatever you prefer
Override conflicting: true
Still check the records of the websites in the Domains tab. Change them manually if not matching the above.
In the Domains tab of the CTL website, put the following:
type: TXT
Hostname: spf
Value: v=spf1 include:spf-c.mailbaby.net ip4:yourip4.1 ip4:yourip4.2 ip6:yourip6:1 ip6:yourip6:2 ~all
TTL: whatever you prefer
Disclaimer, the ip4 and ip6 might not be required, I just put them in for good measure for every server that runs the Email role. Any mailserver changes, I just update only this record, as all the others point to it. 'Chaining' the includes is fine. This also assumes you let Enhance run the DNS on the domains not connected to Cloudflare. The CTL website 'hostingcompany.com' must use Enhance's own DNS via Enhance DNS role or have Enterprise level Cloudflare subscriptions.
If that still gives errors you've got the investigate the errors from the Mailbaby interface. It also never hurts to test stuff with something like https://www.mail-tester.com/ as they always accept your email and tell you exactly what's wrong with it, like DKIM, DMARC, lack of SRS or who knows what can go wrong with email nowadays.
