The title is a duplicate but my question is different.
The same project works fine and is allowed to be built on
buildToolsVersion 23.0.3
if I hadn't upgraded my android studio to "2.3.Beta 2" I could still build with 23.0.3?
Yes.
You can still run the build process from command line with any version of build tools.
Feel free to upgrade build tools to 25.0.2 (latest as of 27.1.2017). This only affects build process, it doesn't affect the app behavior.
Newer versions of build tools incorporate more options and newer technologies and newer versions of Android Studio depend on these technologies.