If you follow the instructions and send the message asking them to disable it, you'll get the following response (tried it on two accounts):
Hi,
Thank you for contacting Outlook.com Support. My name is Jayesh and I will be helping you with your issue today. I understand you
are wanting to turn off the 'Safe Links' feature.
The Outlook.com team has enabled premium features for Office 365 subscribers, including no ads and advanced email security. As part
of these updates, you now receive a higher level of protection against malware and phishing threats. The Outlook.com service scans each link you click in your emails, and if the destination website contains suspicious content, you will be redirected to a warning
page. We recommend that you do not proceed to any sites that trigger the warning page.
As part of this change, the links in some emails you receive will look different. The links will contain additional information related
to the security checks that were performed. Over the coming months, new Outlook.com updates will improve the appearance of these links while still keeping you protected.
At this time, Outlook.com doesn't provide an option to turn off advanced security on the links. If you're not able to use the links,
I can refer this ticket to our escalation team to review.
Thank you for your patience while the Outlook.com team works on improvements to the experience.
For more information about the Outlook.com Premium security features, go to https://support.office.com/article/Advanced-security-features-in-Outlook-com-Premium-551ddf23-7f35-4697-8a71-30b3359362dd
https://products.office.com/en-us/exchange/online-email-threat-protection
Please let me know if there is anything more I can help with.
Best wishes,
JAYESH K.
Outlook.com Support