Is it legal to be paid salary but have your shifts scheduled by your manager?

As long as your salary is at least equal to minimum wage, it is entirely legal. In fact, if shifts have any meaning in your job, and you HAVE a manager, they schedule your shifts.

The laws vary from state to state .  Look up your state regulator for employees on the internet and see if you can get real answers to your questions .  Their are federal employment regs. also .

Of course it is legal. Being paid salary does not in any way indicate that you have a set schedule or that the shifts have to be consistent. That said, if you work over 40 hours, it is possible you may be eligible for OT.

WHERE - it might matter.

In MY State there is no "flat salary" law concerning inconsistent shifts.

If you are not paid overtime, that's a legal problem.

Yes, it's legal. Your friend is wrong. What can't happen is you not getting your full salary if you don't show up for all of those shifts. If you're on salary, the employer must pay you a week's salary if you perform any work in a week at all, regardless of quantity or quality of work, meaning if you don't show up for one of your scheduled shifts, the employer can't dock your pay. The only way you won't receive your full salary for a week is if you don't come to work at all during that week, but if you show up and work at all during a given week, you're entitled to your full salary for that week, meaning if you're paid biweekly, for example, you're entitled to a week's worth of that salary if you show up and work at any time during that week and for both weeks if you show up and work at all in each of the weeks.  That's why salaried employees often get an allotment of paid time off that they are to use when they don't come to work for a scheduled shift-- because the employer can't actually dock your pay for not working all of your scheduled hours. The allotment then becomes a means for disciplining and/or terminating employees that miss too much work, the threat generally loomed being that if you miss scheduled shifts over and above the paid time off the company allots, you're fired.