Kids do need consistency, but here's something I've learned from watching kids very carefully during my 63 years: They need consistency from each person individually, not from all persons collectively. By the age of two, if not earlier, their little brains are busily cataloging all sorts of input, including the kind of behaviors/reactions they can expect from Mom and Dad, other family members young and old, and the family dog and cat.
Individuals who run hot and cold in unpredictable ways do baffle and create havoc for kids emotionally.
But they are very well equipped to sort the rest out. Little kids do NOT expect the same feedback from every other living thing, and from an early age, they do not expect the same feedback from all caregivers. While one consistent set of rules might take root a bit faster during the child's early training, it would also be misleading and probably detract from the child's flexibility and ability to adapt to different situations. Think how baffling it will be the first time a babysitter, a teacher, or even another set of parents at an overnight for a child who has no experience with different people behaving differently or holding different standards.
I read an intriguing book a few years ago, Island, by Aldous Huxley, in which an idyllic society had learned to raise children with great awareness to every child's emotional needs. Understanding that no one set of parents was going to be free of all flaws and mistakes, the whole society had adopted the understanding that other adults would be available (often by the child's choice) to provide a more whole and rounded experience. While I think the ideals in that story are a bit beyond reach for our times, the author still made a very compelling case for "it takes a village to raise a child," and is very much within my own life observations.
So, I hope you can relax a bit and let grandparents be who they most authentically are at this stage of their lives. Those connections can be wonderful and enriching for your child, even if they do things differently. Perhaps even BECAUSE they do things differently. Some will be more lenient, some will be stricter, but unless they are doing something that's truly negligent or abusive (in which case you'd be unlikely to leave your child alone with them), they are helping to round out your toddler's experience.
And that's a good thing, when all is said and done.