In fact almost any tax measure will distort the economy (from the path or process that would have prevailed in its absence). For example a sales tax applied to all goods will tend to discourage consumption of all the taxed items, and an income tax will tend to discourage people from earning money in the category of income that is taxed (if they can manage to avoid being taxed). Some people may move out of the work force (to avoid income tax); some may move into the cash or black economies (where incomes are not revealed to the tax authorities).
The discussion about fiscal neutrality therefore really concerns tax measures that introduce distortions into the economy or society that raise serious doubts as to the wisdom of the tax measure. For example, in Western nations the relatively affluent are taxed partly to provide the money used to assist the relatively poor. As a result of the taxes (and associated subsidies to the poor), incentives are changed for both groups. The relatively rich are discouraged from declaring income and from earning marginal (extra) income, because they know that any additional money that they earn and declare will be taxed at their highest marginal tax rates. At the same time the poor have an incentive to conceal their own taxable income (and usually their assets) so as to increase the likelihood of their receiving state assistance. It can be argued that the distortion of incentives (the move away from a fiscally neutral stance that does not affect incentives) does more harm than good.
One of the main distortions sometimes said to have arisen in the USA and the UK as a result of tax policy is the creation of a permanent underclass, dependent on welfare and discouraged (by the tax system) from seeking work and betterment. In some countries the tax system can be badly designed to deal with such issues, e.g. sometimes the marginal tax rate that applies to earned income (as someone takes work attempting to escape from unemployment and welfare) is so high that the persons take-home income (post-tax and after taking account of any benefits or welfare receipts) does not increase as a result of taking work.
There was an example of distortion of the economy by tax policy some years ago in the UK when cars supplied by employers to their employees were taxed at advantageous rates (e.g. encouraging the growth of company car fleets). Over several years the distortion grew to the point that the majority of cars used by working families were company cars and the dealership structures, and even the types of cars used, altered to adjust to the tax regime.