The standard economics story, as I understand it, is that deficit spending increases inflation because it is increasing demand chasing limited supply.
Yes this is more or less correct. In standard mainstream New Keynesian models, besides other things like expectations, inflation is result of increases of aggregate demand, or decreases of aggregate supply or some combination of these.
Wouldn't the MMT suggestion also be valid since taxation also removes money from the economy so that there is less demand for limited supplies? It makes sense to me that taxation is deflationary.
Am I misunderstanding MMT?
There isn't an rigorous accepted model of MMT that someone can point to so its difficult to know what MMT as a theory is saying. MMT would not strictly speaking be considered 'separate' theory, in fact multiple authors pointed out its indistinguishable from old Keynesian models with some very 'strange' assumptions about parameters that old Keynesians did not accept e.g. it implicitly assumes kinked aggregate supply and so on (Prinz & Beck, 2021, Palley 2014)).
However, some MMT proponents like Kelton do claim that (e.g. see her book Deficit Myth).
If I am understanding MMT correctly, is this point accepted by establishment economists?
It is not generally accepted for taxation to be deflationary a priory. Taxation does not affect just aggregate demand but also aggregate supply. So the overall effect is ambiguous. However, if you only look at demand side, it is accepted that taxation itself suppresses aggregate demand provided government does not spend that money. That is another point of contention, where MMT proponents like Kelton advocate for large government spending at the same time (again refer to the Deficit Myth). In mainstream models taxing and spending the money does not reduce inflation.
As a consequence of this and other claims, MMT is generally not accepted neither by mainstream or also other heterodox strands of economics like post-Keynesians (e.g. see Mankiw 2020; (Prinz & Beck, 2021]1; Palley 2014).
If not, what is the argument against taxation being deflationary?
There are several problems here;
Yes taxation does reduce aggregate demand but it also affects supply side. It is well documented that increases in sales/VAT, and increases in corporate taxes, and other taxes as well empirically lead to higher prices and hence at least temporary inflation (see few random examples like (Carare & Danninger, 2008, Baker, Sun & Yannelis 2020)., this is generally well empirically established). This is despite the fact hat they also suppress aggregate demand. The reason for this is that these taxes ultimately increase costs of production and hence firms are willing to supply less goods at the same prices (supply shifts to the left) and this is inflationary.
You would need to suppress aggregate demand more than aggregate supply which is possible, but you have to go through 'vicious' cycle, where you are trying to suppress demand more than the damage you are doing to supply. In MMT this does not happen because under the translation of MMT rhetoric to models like in Palley, their AS is first completely flat (hence changes in AD do not result in any inflation) and then once you hit full employment you get perfectly vertical AS and only then you get inflation and it is unaffected by taxes. In mainstream models you have increasing AS in short run and vertical in long run and both move to the left as a response to higher tax rates. Hence in the MMT model you only need to suppress AD up till you get to the point of full employment, but in mainstream models with upward sloping short run and vertical AS in long run that responds to inflation you will always get some inflationary pressure when you raise taxes.
In micro models taxes create deadweight loss to the economy whereas changes in interest rates (provided they reflect market forces) do not. As a result, even if we can suppress AD more than AS, this method of controlling inflation is less optimal then monetary policy.
Even if you do not believe in mainstream theory, its just empirical fact that tax hikes on corporations, goods, wages and other economic activity generally result in higher prices than otherwise. Hence even if you do not believe in mainstream synthesis of New Keynesian macro and neoclassical micro economics, your theory still has to somehow account for this observed fact.
MMT also ignores various public choice problems. Usually economists support monetary policy over fiscal policy because central banks are technocratic institutions governments aren't. Even in MMT you must ensure you do not go beyond point of full employment with government spending or you will get inflation. It is unrealistic to believe that democratically elected politicians will be able to somehow find this right balance.
From mainstream perspective this also crates double whammy, not only that taxes suppress AS which leads to higher prices but also government spending cancels off at least some of the impact that taxes have on AD. In fact depending on parameters of the economy, it could even further stimulate AD.