Since you have placed this in the “business” section, I assume that you are asking about it in this context. I completely agree with the Civil Rights Act of 1964 (I assume that is the one you are talking about) although I would argue that there are ways in which it is not very effective.
I agree with this act because there is no reason that businesses should be allowed to discriminate on the basis of race or any of the other categories mentioned in the act. It is simply wrong to discriminate on the basis of race.
One problem with the act is that it is not necessarily very effective, particularly today. Any firm can surely discriminate against anyone it likes in a de facto way. The firm does not need to have any discriminatory policies and it does not need to say anything discriminatory. All it has to do is consistently find reasons not to hire minorities. Since most hires are made on subjective grounds, this is easy enough to do.
A second problem with the act is that it does not prohibit discrimination on the basis of sexual orientation. I do not believe that firms should be able to fire people because of their sexual orientation. This is something that ought to be added to the list of protections.
Overall, though, I agree with this law.