Sure, the biggest implication is now we can look for symmetries in the universe and deduce a conservation law (with much difficulty by people way better at maths than me). This conservation law is not going to be broken by further refinements of our models, as it is inherent to the system. For example, you probably learnt about conservation of energy when learning Newtonian mechanics, but since this is a product of symmetry (in time iirc), then future refinements such as special or general relativity won't break conservation of energy. The only way it could is if the symmetry is not fully accurate, like in quantum, where fluctuations in energy are possible, but very minor (providing phenomena such as the Casimir effect).

Most of the details are beyond me, and the maths certainly is, so please don't take my interpretation of the literature as gospel!