Economists generally agree the minimum wage is silly and should be abolished. There does need to be something to replace it, though.
There's a theoretical argument to that effect, but in practice it is not at all clear that holds (it appears not to, which suggests that there may be something wrong with the theory, the main problem being that it is a fundamentally microeconomic argument, and the economy is a macroeconomy, not a microeconomy, and what may apply to a part does not necessarily apply to a whole):
https://www.nber.org/papers/w4509
Insofar as there is a potential problem with minimum wages, I would say it is more related to potentially increasing prices/inflation by raising labor costs, rather than reducing employment.
Minimum wages may also have some other positive side effects, such as stimulating technological change by giving firms more of a reason to adopt new production technologies that are more efficient/automated/capital-intensive and require less low-skilled labor.
I'm well aware of the minimum wage literature. You can find an empirical study showing just about whatever you want. Surveys of economists suggest a dim view on the minimum wage, for example: https://www.epionline.org/studies/survey-of-us-economists-on-a-15-federal-minimum-wage/
Most economists may be tepid about simply repealing the minimum wage without anything else in place, but almost all would leap at the chance to replace it with something better which eliminates the market distortions it generates.First, the particular survey you are linking too is for a $15 minimum wage, which is on the higher end of current proposals. Personally I even am not totally supportive of that, but not for reasons that have anything to do with it supposedly increasing unemployment (rather, an effect on prices would be the issue that is of greater concern). So just chalking up any hesitancy about moving immediately in one step to a $15 minimum wage among economists to the belief that the minimum wage causes unemployment is not a very good argument.
Secondly, since you seem to agree with me that there is no clear evidence indicating that minimum wages at normal/reasonable levels increases unemployment (you say "you can find an empirical study showing just about whatever you want."), then your argument ultimately reduces down to the argument that many economists are ideological/theoretical hacks who believe things without evidence solely on the basis of questionable/abstract/unrealistic theoretical arguments, and try to apply those theoretical arguments to the real world, despite many enormous differences between their theoretical world and the real world. It may well be true that some economists (and even quite a lot of economists) are hacks like that, but doesn't support the argument that the minimum wage causes unemployment.
I would say nuance, as opposed to contradiction. Also, automation and substitution towards capital need only reduce employment if policymakers fail to provide sufficient aggregate demand (if that is a problem, I would suggest increasing aggregate demand, so that we can have both automation/efficiency and employment).
In general, regardless of whether we consider something to be good in bad, if we are smart and intellectually honest, in general we should hope to be able to recognize positive/negative side effects even of things we oppose/support.
As far as my own position goes, I don't really oppose raising the minimum wage by reasonable amounts, but I also am not the most enthusiastic about it. It is good politics, though. The main issue from my perspective is that the minimum wage sets a nominal wage, not a real wage. Raising the minimum wage temporarily to a higher nominal level (but not continuously increasing it) will just result in a temporary increase in the real minimum wage while costs and prices gradually adjust, and then eventually prices will rise to match the new higher nominal minimum wage, and we'll be back with the same real minimum wage (more or less).
If you want a higher minimum
real wage, which I would think is what most people really mean when they say they want a higher minimum wage, then to maintain that you need to keep continuously increasing the
nominal wage further and further. And if you continuously increase it at a higher rate, then you should expect higher inflation.
Personally I would say the great majority of people are overly fearful of inflation, and that reasonable levels of inflation are not actually bad (and can even have some good effects in moderation), but unfortunately if we start getting too much inflation then a lot of reactionary Conservatives (plus the Fed) will start going nuts. However, if reactionary conservatives/the Fed are willing to go along with it without going nuts, I would be fine with continuously increasing the minimum wage at some reasonable rate of growth. But in practice, they are not going to want to go along with it, and we'll get inflation panic leading to all sorts of bad things such as the Fed trying to cause a recession and more people voting Republican.
So personally, if I had a choice and hypothetically had the power to implement whatever policy I wanted, I would rather do other things like increase the EITC or whatever else of various other options that wouldn't work via increasing nominal labor costs.
But none of that means that the minimum wage causes unemployment - it just means that it has potentially adverse political-economic side effects because it contributes to inflation.
