The constitution only "protected" the minority - by limiting government action - because the majority shares a democratic consensus that those rules should be followed, even if they go against some particular law they support. Otherwise, they could have simply forced the issue, even in violation of the constitution. Besides, the constitutions themselves have ways for the majority to amend them.
The constitution is just a mechanism for the citizens to have a better defined set of shared democratic beliefs. It doesn't have magical protection powers.