The Laffer Curve is pretty obviously trivially a real thing, the contentious part is the parameters defining the curves and/or points in multidimensional tax policy space where the Laffer Curve hits a maximum of tax collection and where variation leads to decreases (or no change if there is a ridge maximum and the change exactly follows it.)
Well, also the usual one-dimensional presentation of the tax-policy space that goes with the curve, but that's not so much contentious as obviously wrong.
The people who think it is important tend to have a religious faith that the status quo is in a space where decrease of taxes in any aspect of tax policy moves is back toward the maximum, which, even if you accept the existence of the Laffer Curve, is a claim which needs a lot of justification which is never offered.