You should verify that python27 is coming from SCL and not elsewhere.
In my case I am using CentOS 6, but the process is the same.
So:
$ yum info python27
Loaded plugins: fastestmirror, priorities
Loading mirror speeds from cached hostfile
6 packages excluded due to repository priority protections
Available Packages
Name : python27
Arch : x86_64
Version : 1.1
Release : 25.el6
Size : 5.2 k
Repo : centos-sclo-rh
Summary : Package that installs python27
License : GPLv2+
Description : This is the main package for python27 Software Collection.
We can see it comes from centos-sclo-rh and so is the right version.
We can install this. Because it's from SCL it will install into /opt/rh and this will not impact any other aspect of the OS:
$ sudo yum install python27
...
$ ls /opt/rh
python27
We can see the default python is still unchanged:
$ /usr/bin/python --version
Python 2.6.6
Now we need the scl command. This is from the scl-utils package, which you may need to install (yum install scl-utils).
$ scl enable python27 bash
This runs a new shell with the path changed:
$ scl enable python27 bash
bash-4.1$ echo $PATH
/opt/rh/python27/root/usr/bin:/usr/local/bin:/usr/bin/X11:/etc:/usr/local/sbin:/sbin:/usr/sbin
bash-4.1$ command -v python
/opt/rh/python27/root/usr/bin/python
bash-4.1$ python --version
Python 2.7.8
So enabling and running SCL does not impact the core OS; it won't break anything you normally run but allows for a newer version of python to be installed in parallel (in /opt/rh).