Is Oracle JRE safe?

Yes and no.

Java has historically been more prone to bugs than most standard programs that run in environments that they control fully.

Having said that, Java (and the JRE) have been around for 20+ years, and a lot of the stupid system and environment-level stuff that caught us in the 2003–2005 time frame has been eradicated over the years.

Any software (java-based or other) is only as good as the programmer makes it. There are more C, C#, C++, Python, SQL, RUby….. developers than strict Java developers. How good are the (comparatively small) number of Java engineers?

My answer – Yes, safe, but with an asterisk.

Circa 2005 when installing Java on a Windows machine was the norrn, my laptop was infested with a pernicious Java virus/worm/bug/whatever. I wiped the hard drive clean and re-installed Windows twice and found that installing Java brought back the infestation. Forgoing Java always prevented the problems.

Ever since I abstain from enabling Java. No regrets.