For those of you who might want a refresher on what, exactly, a "conditional" is and why it wouldn't take the same verb tense in both parts, verilyverity did a tremendous writeup on conditional verbs here that is well worth a read. Go on, I'll wait.
Okay, for those of you who didn’t click the link, I’m lifting from verilyverity’s helpful explanation: “All conditionals are built from one independent clause and one subordinate clause that starts with ‘if’ or ‘when’. The if-clause defines a condition, and the main clause describes an outcome that can happen only if the condition is fulfilled.”
Cordelia: Well, you'll be okay here. If you hang with me and mine, you'll be accepted in no time. Of course, we do have to test your coolness factor. (Buffy the Vampire Slayer, "Welcome to the Hellmouth")
The principal clause, “you'll be accepted in no time,” is a direct outcome of the subordinate clause, “If you hang with me and mine.” Notice that the “if” clause is in present tense, while the outcome is in future tense. This makes sense, as the outcome is yet to happen.
In all of the conditionals discussed by verilyverity, the outcome is hypothetical. The verb tenses of the principal and subordinate clauses are not the same and are determined by the likelihood of the situation. It seems complicated, but most native English speakers correctly use the proper verb tense, simply because we grew up hearing it. For these constructions, it is neither correct nor more colloquial to use the same tense in both parts.
There are, however, “if” constructions that do use the same tense in both parts: when the outcome is factual or constant. That is, if you are stating a truth instead of the outcome of a specific situation with varying degrees of likelihood.
Chris: You know what the key is? If Dr. Clark doesn't understand your experiment, he gives you higher marks so it looks like he understands your experiment. 'The Effects of Sub-Violet Light Spectrum Deprivation on the Development of Fruit Flies'? That should do the trick. (Buffy the Vampire Slayer, "Some Assembly Required")
This is meant to be not a prediction of a likely event but as a constant: Dr. Clark always behaves in this manner. Therefore the present tense is correct for both phrases. It would also be correct, however, to predict the outcome as a result of this specific action.
If Dr. Clark doesn't understand your experiment, he'll give you higher marks.
It's a subtle distinction, and which you would use depends on whether you intend to state a general fact or discuss a specific situation.
Now let's take a look at the example given:
If you don't mind, I want to come with you.
It's quite interesting. Here we have an "if" sentence with the same verb tense in both parts, yet it is not stating a constant truth. So what's the deal? This: It is not a conditional. The speaker wanting to come with is not a result of the other person not minding, nor is it something that has not happened yet. A conditional sentence would read "If you don't mind, I will come with you." The presence of "if" in the subordinate clause does not automatically make a sentence conditional.
So, yes. In certain circumstances it can be correct for both parts of an "if" sentence to be in the same verb tense, but it is a matter of sentence type, not of colloquial speech patterns.