Java

Some sites still require it, Why?

A) Java in the web browser - Bad!

Bad because in a web browser you are dynamically downloading Java code from a web site which can change between visits, or because you have Java in the web browser, a web site banner ad might run Java. While web browsers try to sandbox all web based scripting, the Java browsers extensions have proven to be difficult to keep web based Java code out of personal computers.

Basically with Java running in your web browser, you do not get to decided what Java code is allowed to run, and evaluate if you trust the source of that Java code.

B) Java used by an applications you obtained from a trusted source - Good.

Good as in this case, Java is no different from any other programming language used to create an application. You get to decide to download and install the App. And Java in this situation is no more dangerous than any other programming language.

NOTE: I would suggest you just not go to web sites that require Java in your web browser. If it happens to be your bank or other financial institution, I would seriously consider switching to a different bank or institution.

I have removed all Java web browser extensions from my system. But I do have Java installed for some applications I use.

No.

Because they use it to run things on their site.

This is the Java 6 installer if you need it: Download Java for OS X 2017-001. Most Adobe apps require this. Otherwise, you will find the most current version of Java at the Oracle.com site.