It is important to note the difference between "civil rights" and "civil liberties." The legal area known as "civil rights" has traditionally revolved around the basic right to be free from unequal treatment based on certain protected characteristics (race, gender, disability, etc.) in settings such as employment and housing. "Civil liberties" concern basic rights and freedoms that are guaranteed -- either explicitly identified in the Bill of Rights and the Constitution, or interpreted through the years by courts and lawmakers. Civil liberties include:
* Freedom of speech
* The right to privacy
* The right to be free from unreasonable searches of your home
* The right to a fair court trial
* The right to marry
* The right to vote
One way to consider the difference between "civil rights" and "civil liberties" is to look at 1) what right is affected, and 2) whose right is affected. For example, as an employee, you do not have the legal right to a promotion, mainly because getting a promotion is not a guaranteed "civil liberty." But, as a female employee you do have the legal right to be free from discrimination in being considered for that promotion -- you cannot legally be denied the promotion based on your gender (or race, or disability, etc.). By choosing not to promote a female worker solely because of the employee's gender, the employer has committed a civil rights violation and has engaged in unlawful employment discrimination based on sex or gender.
As you can now see, and hopefully understand, Civil Liberties are what are denied to Illegal Immigrants, however they may poses some Civil Rights. Legal Immigrants do retain Some Civil liberties while also receiving all Civil Rights.