Is stress interview a red flag - Yes, if you are hired for a technical position. I don't have experience with any other, so cannot speak of that.
Think about this. When you approach a master in martial arts, does he/she immediately hit you in the face in order to prove their mastery? When you sign up for martial arts courses, do they beat you well to test if you are in good condition to train?
If an interviewer has any background in psychology, whether formal or not, it is extremely easy to tell whether person is being stressed out or not. Things like odd body movements, changes in tone of voice, facial expressions etc. - unless you were specifically trained not to show your emotions, you will show them guaranteed. Even people with 15 years of experience - well I can only say for technical background anyway.
Now, is it important for you to (know how to) work well under stress? Or - is it more important for you to do the work and become better at doing said work? Stress or work - you cannot choose both. Many people I know who are excellent at handling stress are nowhere near as productive as other "sensitive" individuals. Talking 100 times here. A quiet and comfortable work environment is key requirement for measurable personal and professional growth.
There was a good comment by someone on the net about interviews and your first impression.
How they treat you during an interview is the best treatment you'll ever get after and if you get a job with them.
It may get slightly easier when you get a job, but you may later reach a point when they increase stress arbitrarily, just because it's okay and "how things always been done here". Then you need to factor in bad sleep, being sick, kids & family and how all this fits together, when you (often) get a "bad day" at a job like this.
Another way to approach it is what I call a fair treatment principle. If they have doubts about you (and hence testing your stress abilities), doubt them from your side. Are they really good and worth your time? Example questions to ask yourself:
- Do they have 30 days of vacation per year?
- Does it pay 200K/year to work there?
- Can you work from home any time you want?
If you answered yes to all, maybe it is okay to accept their stress requirement. If not, weigh pros and cons, factor in the stress and assume it will always be there. Is everything else worth it? This decision is personal - only you can tell.