Data science, database administration and the web are stable careers if you're competent. Every company has to process some data in some form or fashion, so obviously you can get paid doing data science or database administration(DBAS). Just to be clear, database administration and data science are two different things. DBAS oversee the company's database/databases. Data science is more about processing and analyzing data. They can overlap to some extent, but they are two different jobs. Data scientists focus more on analyzing the data retrieved from the database.Data Science is more mathematics oriented, specifically statistics, than the typical web career, so if you don't like math, you probably don't want to go that direction. On the other hand, just about all companies are moving things to the web and if you are skilled at what you do, you can be paid handsomely.
If you are mediocre, then yes, you can be easily replaced in all three of those fields. Can web development be outsourced and can the field be unstable? Sure, but a company will find it very difficult, especially smaller companies, to let go of a highly competent web developer and ship everything to India or some other country. Why? Because of communication issues, time zone issues, and it can a lot more difficult for the owner to get the changes he wants do to some of the aforementioned issues. If you are the guy who pretty much controls the front end or the back end, then it's going to be hard to fire you.
It will also be hard to get in the door because bootcamps and the such are flooding the market with candidates at the lower end. That's why I'm recommending that you choose something that you really enjoy, because you will have to end up separating yourself from the pack. Most jobs in the industry want something like 3 to 5 or more years of experience and a long list of requirements. Find out which one you can spend your free time outside of work learning about and enjoying.