Here's why, Kevin --

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Amendment I
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
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If you say that discrimination is part of your religion, you are protected under the first amendment, even if it violates other laws. (However, prohibitions against physical harassment, etc. are deemed to be higher laws.) Beyond the right to vote, there are no protections in the Consitution based on race or gender. Sometimes the Equal Protection clause is cited:

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Amendment XIV
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
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But this doesn't really protect rights, it only requires that a state cannot take them away if federal law gives them. The Equal Rights Amendment was never passed. In other words, if the US Congress passes law tomorrow saying women cannot hold jobs, it's perfectly Constitutional, but the state of say, Alaska, can't do it.