Lower taxes can reduce inflation, but they can also increase it. It all depends on the marginal cost of the next widget. So long as the marginal cost is less than the average cost, more demand lowers the average price. To the extent that lowering taxes reduces the cost of doing business and/or increases the spending power of consumers, it is anti-inflationary. OTOH, if the marginal cost of the next widget is higher than the current average cost - because there is a shortage of some input, including labor - then reducing taxes increases demand but not supply, and inflation happens.

Whether a tax loophole that effectively lowers the costs of MNEs lowers prices depends on what the company does with the money. If the company has excess capacity, it may lower prices, which increases demand, which absorbs that excess capacity, which lowers prices in a virtuous spiral until there is no more excess capacity. Then, the increased demand become inflationary and it's time for the Government to impose taxes to reduce demand.

From an economic standpoint, there is no reason to tax corporations. The rule for partnerships - tax the partners - makes the most sense. But taxing the individual owners of publicly held companies is simply impractical. So we tax the corporations instead. Politicians pretend that the corporation is a taxpayer - it is really a tax collector - is just part of how our species rolls.