Am I required to grant an employee's request that he not be scheduled to work on Sunday because of his religion? We operate seven days a week.
Possibly.  Employers covered by Title VII are required to provide a reasonable accommodation for the religious beliefs or practices of an employee, unless doing so would create an undue hardship on the employer's business.  Depending on the facts, it may be reasonable to revise the schedule so that this employee is not required to work on Sundays.  Other reasonable methods of accommodating the employee's religious belief against working on Sundays could include permitting him to voluntarily swap shifts with other employees or permitting him to use paid or unpaid personal leave.  State and local laws should also be consulted as these may impose more stringent requirements than Title VII.
Several employees have complained about a co-worker's frequent proselytizing. I've told the employee that she must stop these conversations because she is making others uncomfortable, but she refuses, claiming her religion requires her to share her beliefs. Am I required to permit her proselytizing?

Not if other employees have complained about the proselytizing.  Title VII requires employers to reasonably accommodate the religious beliefs or practices of an employee unless doing so would create an undue hardship.  Courts and the EEOC have recognized that workplace proselytizing can create an undue hardship if it interferes with another employee's work or if other workers find it harassing.

 

A new employee has asked that she be permitted to wear skirts in our manufacturing plant instead of pants as required by our company's dress code, because her religion prohibits her from wearing pants. Am I required to grant her request?
Possibly, depending on the reason your company requires workers to wear pants.  Employers covered by Title VII are required to provide a reasonable accommodation for the religious beliefs or practices of an employee, unless doing so would create an undue hardship on the employer's business.  If you require employees to wear pants because of a legitimate safety concern, such as a history of accidents that have occurred due to skirts getting caught in the plant's machinery, granting the request could create an undue hardship.  Whether you are required to grant this request depends, in large part, on the specific facts of the situation.  State and local laws may provide different or additional protections to employees.