A major reason economists have issues with MMT is that MMT rejects empirical results about interest rates

The economic consensus about the rate of investment is that it is a downward sloping function of the real interest rate, i.e. investment goes down as the interest rate goes up. You can see an illustration of this in the bottom left plot in the graph from the Wikipedia article on the IS-LM model.

However, MMT proponents reject this. For example, Stephanie Kelton, who is a professor at the Stony Brook University School of School of Communication and Journalism and author of the Deficit Myth, has expressed this view.

In particular, she was involved in a public argument in the pages of the New York Times and Bloomberg with Paul Krugman, who challenged the above view. Her articles are paywalled, but she has published some of them on her website.

In her article Paul Krugman Asked Me About Modern Monetary Theory. Here Are 4 Answers. she specifically states:

#2: Is there no ability to substitute monetary for fiscal policy? Answer: Little to none. In a slump, cutting interest rates is weak tea against depressed expectations of profits. In a boom, raising interest rates does little to quell new activity, and higher rates could even support the expansion via the interest income channel.

#3: Does expansionary fiscal policy reduce interest rates? Answer: Yes. Pumping money into the economy increases bank reserves and reduces banks’ bids for federal funds. Any banker will tell you this.

The evidence suggests that interest rates don’t matter much at all when it comes to private investment: J.P. Morgan (here and here), the Reserve Bank of Australia (here), the Federal Reserve (here) and the Bank of England (here). It is even possible, as MMT has shown, that cutting rates could further slow the economy because lowering rates cuts government expenditures (interest payments), thereby exacerbating contractionary fiscal policy.

Furthermore, the economic consensus is that expansionary fiscal policy increases interest rates. However, MMT proponent have the opposite view, as stated by Kelton in the same article.

Does expansionary fiscal policy reduce interest rates? Yes, unequivocally. You won’t see it in Krugman’s stylized graphic (below), but it does happen in the real world, where the interbank market exists.

Fundamentally, MMT proponents believe that the monetary policy in the form of the interest rate has no effect on the real economy as outline in Kelton's article. That's why they support a zero interest rate policy by the central bank. That's certainly rejected by the various central banks such as the FED, the BoE, the ECB etc.

So MMT is not just how things operate in the economy as some proponents claim. It rejects many well established empirical results.