In the 32 jurisdictions that have registration by party, here are the number of registered voters in each party and the number of independents:
Democratic: 47,106,084
Republican: 35,041,482
ind & misc: 33,696,700
Libertarian: 652,261
Green: 240,222
Constitution: 129,556
Wk Families: 49,758
Reform: 9,004
oth parties 1,814,973
This data uses the most available figures for each jurisdiction. All are as of September or October 2020, except that New York has no data newer than February 2020, and Massachusetts is August 2020.
In February 2020 the numbers were:
Democratic: 45,715,952
Republican: 33,284,020
ind & misc: 33,530,123
Libertarian: 609,234
Green: 246,377
Constitution: 118,088
Wk Families: 50,532
Reform: 6,665
oth parties 1,712,747
The February 2020 tally is the only one in U.S. history in which the number of voters registered independent and miscellaneous was greater than the number in either major party. But between February and now, Republicans regained their second-place position.
The print issue of Ballot Access News for November 1, 2020, has this information by state. All the numbers in that edition are correct for the state-by-state figures and for the national totals for the Democratic, Republican, Libertarian Parties, and the number of independents. Unfortunately the totals for the other parties, as printed, are not, and the national percentages as printed are not. I forgot to update some of the national totals when I was working with the template of the February 2020 data. A correction will be made in the December 1 issue.