So I know this guy...

May 1, 2019
2,251
3,558
Reno, NV
who, foolishly, ran shielded 22/2 wire through his house! He was unaware that he was suppose to use unshielded 22/2. He may have to re-pull with the correct wire as there is still time for it. Curious. What does happen if you use shielded wire for door/window contacts? The box I ... I mean he ... used does say alarm signal cable and it's not red (I believe fire alarm cable has to be shielded).
 
I installed an alarm in a house that used telephone cable to all of the windows and motion sensors. It has worked well for over 10 years.
Also used a cat 5 cable for the keypad. He was retired from telephone company.

Shielded cable will not hurt, but doubt it is needed.
 
I'd likely use it, being careful to ground only one end of the shield (not both) to earth ground. I'll wager it'll work just fine.
 
Depending on the RF environment, say a local radio station nearby, not grounding one end will create a bunch of nice antennas that will have some interesting voltage levels on them. I don't think it would be a problem for an alarm system, simple DC circuit, but one never knows.