Nixon would probably be a moderate Democrat today
No.
Let's review-
Pro-Choice
Pro Gun-Control (he
actually wanted to "abolish" the second amendment saying "I don't see why anyone should be able to own a revolver in his house)
Strongly pro-Affirmative Action
Created the EPA
Moderate to liberal on immigration
Created the AMT
Supported an individual mandate for health insurance, federalization of Medicaid, and a "public option" for health insurance
Raised the minimum wage
Nixon Shock and price controls
The only things that would be conventionally Republican/conservative about him today are his somewhat hardline on crime/drugs (but a lot of Democrats are like that these days) and his hawkish/anti-Communist foreign policy (but again, not that different from a lot of Democrats these days). Even on foreign policy, compare the overwhelmingly negative response to the Iran nuclear deal from Republicans to Nixon's diplomacy with China and the Soviets.
He's not more liberal than Obama and maybe Clinton is a touch to the left of him, but there really aren't any "Nixonian" Republicans left in significant offices except maybe Susan Collins.