Is it acceptable to run 22/4 security wire along side Cat6 and Coax cables, or is there any possibility for interference?
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 remote 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 frequency1.
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.
1. The value 300 bits/second is emerging from my long-term memory, but I could be conflating it with the speed of the soft modems on security panels
I can only say from experience, but I've never had any problems running cat5e/6 for data/voice and security along with coax in the same bundle. This is in an office environment.
In a sensitive environment like a datacenter environment they would likely be in separate raceways but I wouldn't worry about it in your home.