Anxiety is a bit of an umbrella term for a range of mental conditions that are characterised by excessive feelings of fear, apprehension and dread. As a result, anxiety is a medical condition that cannot be just shaken away, just like depression cannot be cured by being more positive.
Anxiety disorders are shockingly common too. The most recent numbers I could find from the Anxiety and Depression Association of America estimate that almost one out of 5 American adults (18%) suffers from some form of anxiety. That means it is something we ought to keep in mind when building digital interfaces and experiences.
Ultimately, it is difficult to figure out what people will feel uncomfortable with, but there are generic advice we can give to make things more pleasant for everyone—especially people suffering from anxiety:
Remove the notion of urgency. The idea that something is only available for a short amount of time is one of the main causes of anxiety among users. By removing this notion altogether, we can make things less stressful. For instance, if a two-factor authentication code is only valid for 1 minute, it might not be necessary to display a timer counting down. Worst case scenario, the user missed the mark and will ask for another code.
Focus on clarity. The more straightforward the interface and its content, the less stressful it is. Avoid double-negatives and reversed checkboxes and be consistent with phrases and terminology. Stay away from scaremongering like dramatising non-critical actions (such as not wanting to benefit from a promotion), or shaming users for performing something (such as opting out from a newsletter).
Provide reassurance. Any sensitive action should be marked as such (like placing an order, or deleting an entry), and it should be clear whether there will be an opportunity to review before confirming. The ability to undo actions is also helpful to know that mistakes can be made and recovered from.
Ultimately, a lot of the work in that regard is about deeply caring for users and staying away from aggressive marketing tactics which are heavily relying on inducing anxiety. As a further read, I highly recommend reading A web of Anxiety by David Swallow from the Pacellio Group which goes more in details.