The US states typically apply a sales tax or 'use tax' to components which are not consumed in exports. As such, exports will contain some small component which consists of, say, the sales tax paid on a computer amortized over 4 years or the paper folders used in record keeping.
This is the distortion that a VAT (a consumption tax) eliminates, by allowing that tax to be backed out of exports since the final consumer pays the tax and not exports. Imports and domestic products are thus on a level playing field (if the VAT is 10%, the import gets taxed 10% at retail and so does the domestic product). See, for example, this Forbes article debunking Trump's claims that VAT is in any way unfair. It also allows governments to crank up or down the tax extraction knob without unduly affecting trade, which is perhaps a legitimate objection- that it makes it easy to increase taxes. Another criticism, typically from the other side politically, is that it is a regressive tax- usually a flat percentage of consumption.
The amount of state tax in such exports is pretty small but probably not negligible. In Canada, prior to introduction of the VAT (called GST) there was a hidden 12% (usually) federal manufacturer's sales tax that caused a relatively large distortion in favor of imports, but thankfully that is long gone, and in many provinces the provincial sales tax has been combined into a single visible tax at consumption for most products.
The US has no federal sales tax and it is probably virtually impossible to imagine all 50 states agreeing on a harmonized federal-state tax system, so implementing a VAT is difficult in the US, but perhaps not impossible.
There appears to be a current and very deliberate attempt to obfuscate what a VAT actually does (create a level field and back out taxes from exports, allowing recipient countries to impose their own taxes at consumption) and conflate it with protectionist measures such as straightforward tariffs or the proposed complex "border adjustability" tax, the latter explicitly prohibited under WTO rules precisely because it is not a level playing field (imports are taxed and exports are subsidized).
Some countries, in particular those with internal subsidies or currencies that are not fully convertible do tax and/or apply quotas to exports but I'm not aware of any commodities that are treated that way in the US.