Independent Contractor or Employee

The first issue in this case is whether or not the massage therapist is considered to be an employee or an independent contractor. Dream Massage has hired the person as an independent contractor but "exercises complete control over how she does her work", including the provision of clients, materials needed to do the work, and complete control over the massage therapist's schedule.
The IRS defines an independent contractor as follows: "an individual is an independent contractor if the payer has the right to control or direct only the result of the work and not what will be done and how it will be done" (IRS, 2017). The level of control that Dream Massage has over the massage therapist in this scenario is not consistent with the legal definition of an independent contractor. Both the behavioral and financial aspects of the common law definition are consistent with the person being an employee. Thus, it is likely that the massage therapist will be considered to be an employee for taxation purposes.
It is worth noting that the company exerting some control will not automatically convert the worker from independent contractor to employee. However, this case is one where Dream has full control over the worker, and thus the worker would be considered to be an employee.
The second issue in the case is whether or not Dream has violated any employment discrimination laws. Normally, these laws only apply to employees, not to independent contractors, but since the massage therapist is an employee, then discrimination laws would apply (Wood, 2011).
The issue of discrimination relates to the order that she cannot wear her hijab as it violates the company's dress policy. Title VII of the Equal Employment Opportunities Act forms the basis of employment discrimation law. But before examining the issues relating to Title VII and hijabs, as assumption must be made that Dream Massage either operates in multiple states or that it has over 15 employees. If it does not, Title VII would not cover the company, and discrimination protections would fall to state or local laws, and the case does not provide information about jurisdiction. So it will be assumed that Dream Massage is covered under Title VII.
Under Title VII, the business is required to provide "reasonable accommodation" for religious garb, as long as it does not cause the business undue hardship. The company's policy on workplace attire does not count as undue hardship, so it would appear that there is a Title VII violation in the request that the person not wear her hijab (Bahler, 2016). The hijab is not a garment that would create issues in performing the duties of a massage therapist, either, so there is no cause for claim of undue hardship with respect to the safe performance of duties.
Yet this issue is more complicated than it would appear on the surface. There have been cases that have arisen where women have been told not to wear a hijab at work (Aslam, 2011). The individual work in such situations has little recourse, however, unless the case is taken on by a group that has the funding to actually challenge the company in question.
The text of Title VII does say that it would be unlawful to discriminate in terms of "terms, conditions or privileges" of employment, dress code being part of terms and conditions of employment; it is unlawful for the company to tell her she cannot wear a hijab.
Beyond the legal aspects, there are a number of ethical considerations relating to a rigid dress code. First, one can see the logic in a massage company wanting to have certain standards of attire for its workers. There are many "massage" operators that are really more like brothels, and it would be important for any legitimate massage therapy business to ensure that it was never confused for anything like that. A dress code that stipulates a certain modesty or professionalism in attire would be reasonable, and even uniforms would be reasonable if the company wanted to do that.
But ethically, going beyond and trying to dictate things that relate more to appearance veers towards the unethical. Dream has no particular reason to dictate what its employees wear, beyond ensuring that what they wear is professional. Thus, having a rigid dress code is ethically questionable at best.
Having a dress code that specficialy precludes religious garb, however, is clearly unethical because it violates Title VII. For the company to violate Title VII, perhaps thinking that it will not have to actually face legal challenge from someone who needs work and has no real power to hire a lawyer and take their case to court, is most certainly unethical.
In general, companies should not have rigid dress codes but should rather encourage professional attire, and they definitely should not attempt to govern religious garb unless there are legitimate employee safety issues at play. This seems like a situation where Dream Massage was ignorant of the law, though its attempt to also classify the employee as an independent contractor does indicate that they are maybe not ignorant of the law but just trying to circumvent it, which would be unethical behavior according to any reasonable standard of ethics that you could use to evaluate the company's actions.

References

Aslam, S. (2011). Hijab in the workplace: Why Title VII does not adequately protect employees from discrimination on the basis of religious dress and appearance. UMKC Law Review Vol 80 (221)

Bahler, K. (2016) What to do if you're afraid to wear a hijab to work. Time Retrieved October 22, 2016 from http://time.com/money/4572115/wear-hijab-work-afraid-civil-rights/

IRS (2017) Independent contractor defined. Internal Revenue Service. Retrieved October 22, 2017 from https://www.irs.gov/businesses/small-businesses-self-employed/independent-contractor-defined

Wood, R. (2011). Some control won't convert independent contractors to employees. Forbes. Retrieved October 22, 2017 from https://www.forbes.com/sites/robertwood/2011/02/03/some-control-wont-convert-independent-contractors-to-employees/#13de2c434158