I recently installed Python 2.7.3 on a CentOS machine by compiling from source. Python 2.7.3 is installed at /opt/python2.7 and when I installed it I just changed /usr/bin/p
Daniel's answer is probably the most ideal one as it doesn't involve changing OS files. However, I found myself in a situation where I needed a 3rd party program which invoked python by calling usr/bin/python, but required Python 2.7.16, while the default Python was 2.7.5. That meant I had to make usr/bin/python point to a Python version of 2.7.16 version, which meant that yum wouldn't work.
What I ended up doing is editing the file /usr/bin/yum and replacing the shebang there to use to the system default Python (in my case, that meant changing #! /usr/bin/python to #! /usr/bin/python2). However, after that running yum gave me an error:
ImportError: No module named urlgrabber.grabber
I solved that by replacing the shebang in /usr/libexec/urlgrabber-ext-down the same way as in /usr/bin/yum. I.e., #! /usr/bin/python to #! /usr/bin/python2. After that yum worked.
This is a hack and should be used with care. As mentioned in other comments, modifying OS files should be last resort only.