Advanced Threat Protection (ATP) is ruining Outlook.com

To add here is the page with more details - https://support.office.com/en-gb/article/Advanced-Outlook-com-security-for-premium-subscribers-882d2243-eab9-4545-a58a-b36fee4a46e2. The included FAQ says this about disabling these features and it also confirms the behaviour you are seeing:

Can I deactivate these security features?

To provide the best protection for your account, these features are on by default and not designed to be turned off. You can contact our customer service team via in-product support to have them deactivate the features on your behalf, but we do not recommend it.

Why do links in my messages look different?

After you activate the advanced security features, links in your email might look different. For example, in some messages links might appear longer than usual, and include text such as "na01.safelinks.protection.outlook.com." This is related to the checks we perform to protect you from phishing attacks.