We are loyal to our foundations. The foundations of the Church were laid by Christ on the Rock of St Peter and were built on century by century by Peter's successors and the successors of the Apostles. It ties in with the sense of continuity that the Holy Father is trying to build on the foundations of those who preceded him. So, being a 'Catholic fundamentalist' shouldn't be so terrible. It means that you believe in the foundations, the continuity and the Holy Tradition of the Church.
You could argue that as 'Catholic fundamentalists' we are only being faithful to our foundations if we say that sacred music didn't arrive in 1960s and say that we believe the Holy Father is right when he says that Mass being celebrated facing East makes liturgical sense. 'Protestant fundamentalists' with their theology steeped in Reformation thought are being loyal to their foundations. 'Islamic fundamentalists' who wage war and murder in the name of Islam, really, are only being loyal to their foundations too. Religious fundamentalism is a dirty phrase today, but it really depends on your foundations. The countless martyrs of the Church tell us that when they faced shedding their own blood for Christ and His Church, they were being loyal to their foundations. I think that's as loyal to your foundations as you possibly can be.