Was Reagan a True Conservative?

Was Reagan a true conservative?

For instance:

As president, Reagan “raised taxes in seven of his eight years in office,” including four times in just two years. As former GOP Senator Alan Simpson, who called Reagan “a dear friend,” told NPR, “Ronald Reagan raised taxes 11 times in his administration — I was there.” “Reagan was never afraid to raise taxes,” said historian Douglas Brinkley, who edited Reagan’s memoir. Reagan the anti-tax zealot is “false mythology,” Brinkley said.

He gave amnesty to three million undocumented aliens.

He appointed Sandra Day O’Connor who who refused to overturn Roe v. Wade, wrote the Opinion upholding affirmative action at Michigan law school as constitutional, and "was a vigorous defender of the citing of foreign laws in judicial decisions." Charles Krauthammer described her as displaying "political positioning embedded in a social agenda".

Was Reagan a liberal by today's labels? Have the labels shifted to the right, as compared to 30 years ago?