As you imply, the term neoliberal is practically useless since it is defined differently by various groups. It’s often associated with Prime Minister Margaret Thatcher in England, who famously held up a copy of Hayek’s The Constitution of Liberty declaring “this is what we believe” as she slammed it down on a table. Reagan is often taken as her American counterpart.
Reagan cut the capital gains tax in his tax reform bill of 1981 to 20 percent and then raised it again in his tax bill of 1986 to 28 percent. The tax burden during the Reagan administration shifted from upper-income to middle-income taxpayers, mainly because of the sizable increase in payroll taxes in 1983 to fund social security.
There was some re-regulation during the Reagan years. Politicians are willing to sell legislation and regulation to the highest bidders, so naturally there is re-regulation in every administration. But to characterize Reagan’s administration as reducing regulating is dubious. The Garn-St. Germain Act, often cited as “deregulating” the S&Ls in the early 1980s, for example, is clearly re-regulation. Here’s the FDIC page on it:
In contrast to new regulations whose net effect on the regulatory state is controversial, the Monetary Control Act of 1980 increased the regulatory power of the Fed.