A colleague was wondering about a sentence similar to the following (I’ve changed it slightly because it’s from something she’s working on):
If we treat dogs and cats equally, we might expect them to turn out to be friendlier than they would if we treat them differently.
She feels like the second treat should be treated but she’s not sure why.
Here’s why – or why not, depending.
It’s introduced with would and if: “they would if we treated them differently.” It’s set up as counterfactual, so you can’t use the indicative form. The present subjunctive form use the past-tense form.
Would you eat cake? I would if I had one to eat.
*Would you eat cake? I would if I have one to eat.
Will you eat cake? I will if I have one to eat.
(* means “no good”)
The whole sentence is conditional, but there are two kinds of conditionals, and the first “If” is not necessarily a counterfactual: if we are actually proposing doing so, rather than mooting something we don’t see as a present option, then the indicative is the right mood to use.
If pigs had wings, we would need better umbrellas.
*If pigs have wings, we would need better umbrellas. [it’s not possible that pigs have wings]
BUT
If lunch were ready, we would eat. [it’s not]
If lunch is ready, we will eat. [it may be]
We can combine the indicative with the counterfactual in a sentence like the one in question because we’re talking about a real-world possibility and comparing it with something moot.
If we bake cookies, we will make the children much happier than we would if we baked spiders. [we are considering the real possibility of baking cookies; spiders are not actually on the menu]
The remaining issue with the sentence, though, is whether treating them differently is not an option. If we are really considering treating them equally, then the alternative we by implication must be considering is treating them differently, putting the whole sentence in the indicative:
If we treat dogs and cats equally, we may expect them to turn out to be friendlier than they will if we treat them differently.
On the other hand, if we really are just mooting it, not considering the present possibility of real action, the whole thing has to be counterfactual:
If we treated dogs and cats equally, we might expect them to turn out to be friendlier than they would if we treat them differently.
So… determine what’s intended and write accordingly.
Sesquiotica 
If, however, you’re talking about a situation where dogs and cats are treated equally and we’re talking about expected consequences, then it is reasonable to be indicative in the the first “if” and counterfactual in the second “if”. For parallel, consider a situation where you’re trying to tell someone why what they do is bad: “If you insist on working for three hours without saving, you’re going have a higher risk of losing your work than you would if you saved every so often!”
Not to be obstructionist, but what if half of it is counterfactual?
If we treat cats and dogs equally, we aren’t treating them differently. We can’t do both. So, if one is factual, the other is counterfactual, and it seems to me that you could have both in the same sentence:
If we treat dogs and cats equally, we may expect them to turn out to be friendlier than they will if we treated them differently.
Um, somehow your comment didn’t show up – or I was really not paying attention – when I posted mine. Sorry.