Should consensus affect the Supreme Court?

I received an email from the ACLU today that said, in part:

We must demonstrate that there is a national consensus in support of marriage for same-sex couples. Every step forward will make it harder for the Supreme Court is consistent with the Constitution.

Consensus shouldn't affect the Supreme Court, should it?  The inherent flaw in democracy is that the majority can oppress the minority.  The Constitution is supposed to keep that oppression from happening.

I don't care if 99% of people are against gay marriage or black education or .  The Supreme Court should use the 14th amendment to strike down any law that restricts the privileges of citizens.  A privilege is an entitlement granted by the state.  Marriage licenses are granted by the state and entitle citizens to certain benefits.  Seems pretty clear to me that that's a privilege.

Or is the ACLU just being pragmatic?  In an ideal world, perhaps, Supreme Court justices shouldn't be affected by popular opinion, but they are only human, so they probably are affected.