TL;DR it should be OK to run them together.
The signals from a security sensor are typically very low frequency because they're generated by the switch within the sensor opening and closing as the sensor activates. So for a motion detector, it might open and close a few times as you cross the field of view; a door or window sensor would switch as often as you open or close its corresponding door/window, etc.
The signals from a keypad are higher frequency because they have to communicate more information, e.g. the text to display on the screen, or which buttons were pressed on the keyboard, but they're still going to be low frequency.
Twisted pair cables, such as Cat 6, are fairly immune to outside electromagnetic interference, and coax is even better thanks to its outer shield. And since the signals they carry (e.g. Gigabit Ethernet, TV signals, etc.) are very high frequency, the chances of interference with the security system's signals are very low.