Believe me; I understand the nature of that kind of work. I've worked at quite a few call centers, in the past. I know exactly how rigorous that scheduling is to ensure the phones are covered.
The issue I'm bringing up is that the number is less important than the proportion; most places I've worked where this was an issue, we staggered lunches over 2 hours, and breaks over the remaining time. And people generally didn't get breaks during the first/last half hour of their shift. Given the math, that would mean each 15-minute break period within that time could handle the 150 Muslim workers; more than 150 people are gonna be on break at any given time, if everyone's working a 9-5. And if they're working 24/7, the proportions still work out, assuming they're evenly distributed over the shifts (and there's little reason why they couldn't be). Remember; this place employs over 2000 people. 150 isn't a huge chunk. Particularly if you can break that into two groups for back-to-back break sessions, on the off chance that you still can't get them all on one break.