Say that a proposition p is weakly earthly provided that for every pair of worlds w1 and w2 which exactly match one another in respect of all states of affairs localized within a thousand lightyears of earth and all entities and events capable of causally affecting states of affairs localized within a thousand lightyears of earth, p has the same truth value at w1 and at w2. It is very plausible that just about all propositions used in everyday speech are weakly earthly. A sentence is weakly earthly provided it expresses a weakly earthly proposition.
Now, suppose that "If p, then q" is weakly earthly. I shall argue that "If p, then q" has the same truth value as the material conditional. First, observe that if the material conditional is false, so is "If p, then q", since otherwise modus ponens wouldn't work.
For the converse, suppose the material conditional p→q is true. Now imagine a possible world w* which is just like our world, but which also contains a one-way causally isolated island universe u, such that events in our universe can affect events in u but not conversely, and where u contains Frizzy, a being that knows the truth values of all weakly earthly propositions (maybe God has told them all to him), and that believes no contradictions. Moreover, Frizzy has the odd property that he always speaks sentences in pairs. First, he utters a claim with no regard for its truth. After that, if the first claim he had uttered turns out to be something he believes to be true, he utters a second claim that he believes to be true; otherwise, he utters another claim with no regard for its truth.
Now suppose Frizzy utters the pair of propositions a and b (in this order), and suppose a and b are propositions Frizzy knows the truth values of. Then, if a is true, so is b. And, hence, it is true that "if a, then b". But now as long as the material conditional p→q is true, i.e., as long as we do not have both p and not-q, it is coherent with the above description of w* that Frizzy utters the pair p and q. So let us suppose that. Then, as noted above, it follows that it is true in w* that "if p, then q". But "if p, then q" is weakly earthly. Hence, if it is true in w*, it is true in the actual world.
What I have shown is that for any weakly earthly indicative conditional, the truth value of the conditional is equal to the truth value of the corresponding material conditional. Moreover, this argument can be run in any possible world (in some possible worlds, of course, the claim is close to trivial because there are no contingent weakly earthly claims). Therefore, necessarily, a weakly earthly indicative conditional holds iff the corresponding material conditional does. Now, assuming indicative conditionals have truth value it would, I think, be very unlikely that there would be something special in this way about weakly earthly indicatives. (The assumption is needed, because if indicatives don't have truth value, there are no weakly earthly indicatives.)
So, we have very good reason to think that either indicatives lack truth value or else indicatives are logically equivalent to material conditionals. I don't know which disjunct to choose.