Are there any symmetries in rules of Life-Like Cellular Automata? Life-like cellular automata have $2^{18}$ different possible rulesets, and I would like to test hypotheses/search through them all, however that's a lot of rulesets to test a simulation on, so I'm looking for symmetries.
The one symmetry that I know about is black/white rule reversal. Which in short means there exists a rule where the behavior of ON and OFF cells are switched.
It would be very surprising to me if there weren't more symmetries, but I don't know where or how to even begin looking.
 A: By "symmetry", I assume you mean an isomorphism between two rules, such that the evolution of any pattern under on rule can be reversibly transformed into the evolution of a corresponding pattern under the other rule by applying a suitable transformation to the state of the lattice at each generation.
If so, there aren't really that many, because the rule notation already implicitly abstracts away most of them.  For example, rotations and translations of the lattice are automorphisms of any Life-like CA rule, but the rule notation is designed (reasonably enough) to remain unchanged by such transformations.
The on/off state reversal you mentioned is the main one: for each Life-like CA rule, there exists an isomorphic rule whose evolution is identical except that the state of each cell is inverted.  Note that in some cases this may be the same rule, as with the Day and Night rule (B3678/S34678).
For such "self-complementary" rules that are invariant under on/off reversal there does exist another rule isomorphism, obtained by inverting only the output (or, equivalently, only the input) states of the rule.  The evolution of patterns under the resulting rule is the same as under the original rule, except that the states of cells in every second generation are inverted.  (Note that applying this transformation to a rule that was not self-complementary would not yield an isomorphic rule, since the evolution of the inverted pattern in the second generation would be different.)  As this means that the "empty" background of the lattice will blink on and off (if it did not already do so for the original rule), this isomorphism is commonly known as the "strobing equivalent" of the original rule.
By applying both the on/off reversal and the strobing isomorphism, we can in fact find exactly one unique isomorphic pair for every Life-like CA rule.  Thus, the number of such rules up to isomorphism is exactly half of the total number of rules representable by the rule strings.

As far as I can tell, the two isomorphism described above are the only non-trivial isomorphisms of Life-like CA rules on the 8 neighbor Moore lattice.
(Some other automorphisms do exist: for example, for the rule B-/S012345678 that leaves all cells unchanged, every permutation and/or partial inversion of the lattice is obviously a trivial automorphism, and the Replicator / Fredkin rules also have some non-trivial automorphisms.  Such automorphisms can also be combined with the on/off or strobing isomorphisms above to obtain additional isomorphisms between the same pairs of rules, but such composition won't yield any new isomorphic rule pairs.)
On the 4 neighbor von Neumann lattice, where the neighborhood of each cell consists of only the four diagonally adjacent cells, we do have some additional isomorphisms due to the fact that the adjacency graph of the lattice is bipartite.  In particular, for self-complementary 4 neighbor rules, simply swapping the B and S halves of the rule string (i.e. inverting the central input) yields another rule that is "checkerboard equivalent" to the original, in the sense that taking the evolution of any pattern under the original rule and inverting every second cell on the lattice in a checkerboard pattern (alternating the set of cells that are inverted in each generation) yields the evolution of a corresponding pattern under the new rule.
