Andy Clark and David Chalmers are huge in promoting the extended mind thesis but who/what is their main opposition?
What are the main oppositions to the extended mind thesis? and who presents them?
I am not aware of who else opposes the Extended Mind thesis (in fact, I was unaware of it until I read your inquiry), but I would be an opponent thereof. The following illustrates some of the thesis's incongruities.
1. Twofold Absurdity
Consider some mind. It necessarily resides in one and only one person (several individuals may present a multitude of mental similarities, but that cannot negate the "bijective" relation one mind - one person). One consequence of this bijection is that, to speak in terms of set theory, mind x and mind y are pairwise disjoint for any x<>y.
A person's mind experiences (or produces) one idea at a time. In particular, the person does not perceive two opposites (or two opposite effects) simultaneously. For instance, a reasonable person would never sense/describe a one-color object as being both black and white simultaneously.
Now consider the effect that an imprisonment produces on two individuals, criminal C and victim V, where C is imprisoned for committing crimes against V.
The external object jail aids C's cognition of constraint (a constraint which prevents C from harming V again). Under the Extended Mind thesis, the jail is an extension and part of C's mind. At the same time, that same external object aids V's cognition of liberty (now V can live worry-free about C). Under the Extended Mind thesis, that jail is an extension and part of V's mind as well.
Since, according to the Extended Mind thesis, the jail is part of C's mind and V's mind, the thesis fails the aforementioned attribute that two [persons'] minds are pairwise disjoint. Even if that flaw were acceptable, it would still lead to the additional absurdity that one same piece of mind --the extension which C and V allegedly have in common-- produces two opposite effects simultaneously, since constraint is the opposite of liberty.
2. Extended and Dysfunctional
Apropos of the Otto & Inga fictional illustration in the Wikipedia article, another defect of the Extended Mind thesis is that it seemingly ignores notions of autonomy (an important attribute of a person's mind).
Otto's need for a notebook --to remedy his Alzheimer's disease-- evidences his partial lack of autonomy. The thesis purports that the notebook is an extension of Otto's mind.
Now suppose Otto sequentially losses also other cognitive abilities, whence he becomes dependent on a GPS, a dictionary, an automated assistant to read aloud for him, a machine to aid his muscles so that he can walk, and so forth. The Extended Mind thesis would have to consider all these devices extensions of Otto's mind. But this leads to the irony that the gradual extensions of Otto's are coupled with his [authentic] mind's growing inability.
In this sense, the Extended Mind thesis merely advances an euphemism (cognitive substitution) for an intrinsic inability to perform cognitive processes.
3. The Risk of Greater Impunity
Having been harmed by a criminal who alleges mental illness (so as to avert liabilities in court), I can identify one dangerous ramification if the Extended Mind thesis ever were to gain any traction in the legal system.
The thesis would afford criminals the pretext that the unlawful intent did not reside within themselves, but in their "mind extensions"; be it the matchstick that "instructed" them to commit arson, the gun that "ordered" them to do a mass shooting, or (inline with the defendant's nonsense in my case) the electronic devices that "inform" the defendant that the US government and I "keep spying on and conspiring against" her.
Perhaps the Extended Mind thesis ultimately aspires to present some holistic, "quantum", or pantheistic dialectic. But it is questionable whether its proponents can advance some reasonable, useful view that could compensate for the inconsistencies that the Extended Mind thesis introduces.