First, please notice an important point about the rage mutagen:
At the end of each turn that he takes hit point damage, the ragechemist must succeed at a Will saving throw (DC 15, or DC 20 if any of the damage came from a critical hit that turn) or take a –2 penalty on Will saving throws and to Intelligence.
You can only take this penalty once per turn, even if you fail the save. That sharply limits how quickly the penalties grow—encounters rarely last more than 2-3 rounds, so you are not generally looking at penalties larger than –8 to –12 from a given combat. It’s still a big downside, particularly since it lasts an hour so you may very well start combat with penalties from the last one, but it’s not quite as bad as you describe. In particular, most ragechemists probably won’t be knocked unconscious during the typical fight unless they started the fight still suffering from a previous rage mutagen.
Anyway, not as bad is still a long way from good. Ditching those penalties remains desirable. Can mutagenic touch do it?
The first question is whether or not mutagenic touch can transfer the rage mutagen in the first place. This one is pretty clear: the rage mutagen class feature doesn’t let you create some new, distinct thing called a rage mutagen, it just changes how the Strength-improving mutagens a ragechemist produces work. They’re still mutagens. So mutagenic touch should be cool to transfer it.
That’s good. That means you lose the bonuses and the basic Intelligence penalty associated with the rage mutagen, and your opponent takes those but the Strength bonus is halved and the Intelligence penalty is doubled. It also means you stop losing Intelligence, Will, and Dexterity when you get hit, and your opponent starts to do that. Also good. But that leads us to our second question...
The second question is, when you transfer the rage mutagen, do you ditch the penalties you’ve accrued, saddling your target with them? That looks a lot more dubious to me: the rage mutagen still has the regular penalties associated with a mutagen (specifically, to Intelligence). It just also has the drawback of causing these lingering penalties when you’re hit. Those penalties aren’t tied to the mutagen itself—they last far longer than the mutagen does, which means you’re still suffering from them long after the mutagen has expired. They also aren’t described as penalties applied by the mutagen so much as just losses you suffer from your own rage and from the damage.
So I think there is a strong argument, anyway, for saying that mutagenic touch cannot transfer those penalties to your target. It transfers the thing causing you to keep gaining those penalties, so your opponent can start doing so and you can stop doing so, which are both good, but you still have to deal with the penalties you’ve already got.
This is by no means cut-and-dry or absolutely certain. There is also an argument that those penalties do get transferred. After all, no matter how it’s described or how long it lasts, the penalty here is described as part of the rage mutagen class feature. You can argue for the full transfer. I just find the opposite argument a little more convincing.
Ultimately, though, what the rules say is secondary to what makes for a good game. That is going to be up to your GM; you can make your case to him or her (and, if you’re honest about it, admit the alternative argument against your position), but ultimately he or she is going to have to make a call. Personally, the ragechemist penalties seem much, much too large to me; ragechemist looks like a really bad choice of archetype as a result. I would be looking for ways to improve it. But this particular approach worries me—it’s really swingy, putting you in an incredibly vulnerable position with these penalties, and making the Fortitude save that your opponent gets against mutagenic touch a massively consequential roll. Generally speaking, the game works better when no single roll is too important, and I might be worried about that one.
In the end, I would probably recommend against the ragechemist archetype altogether. It’s just kind of problematic. If you really loved the concept, I would probably overhaul it myself to something I find more appropriate to the game—nix the cumulative, lingering penalties, find other bonuses to give that work better with lesser downsides. One neat idea, based solely on the name of the archetype, would be for rage mutagens to offer rage powers, but I haven’t given that a second thought beyond saying “huh, rage mutagen; rage powers. huh.”