Did Democrats take out the words "under God" from the nightly Pledge of Allegiance when it was recited at their national convention? No, that's not true: The words "Under God" were included in the Pledge of Allegiance in nightly prime time events of the Democratic National Convention each of the four nights.
The claim originated in a post published on Facebook on August 20, 2020 (archived here), with following text:
Dems recited our beautiful pledge of allegiance tonight and took out "UNDER GOD" ! What say you!
This is what the post looked like on Facebook at the time of writing:
(Source: Facebook screenshot taken on Fri Aug 21 16:17:05 2020 UTC)
Each of these four embedded videos has been cued to begin playing at the point in the program when the Pledge of Allegiance is recited.
Monday, August 17, 2020 -- The first night of the convention:
Tuesday, August 18, 2020 -- The second night of the convention:
Wednesday, August 19, 2020 -- The third night of the convention:
Thursday, August 21, 2020 -- The fourth and final night of the convention:
There have been other posts on social media that called attention to the omission of the words "under God" from the recitation of the Pledge of Allegiance in two of the nearly 30 caucuses and councils meeting during the convention, the Muslim Delegates Assembly and the LGBTQ caucuses. David Brody, the chief political analyst for the Christian Broadcasting Network called attention to this in two tweets which included video:
NEW! Democrats leave out, "Under God" from the Pledge of Allegiance at the #DemocraticNationalConvention Muslim Caucus meeting this week. Watch delegate AJ Durrani skip it. Featured speakers at the event were @BernieSanders @RashidaTlaib & @TomPerez @realDonaldTrump pic.twitter.com/Ra4SX2cqNy-- David Brody (@DavidBrodyCBN) August 19, 2020
NEW VIDEO: At the #DemocraticNationalConvention , LGBT Caucus purposely leaves out the words, "under God" from the Pledge of Allegiance. Watch. This now makes twice that two key constituencies of the Democratic Party have done this. See my earlier tweet about DNC Muslim Caucus pic.twitter.com/2GIDcCMq1F-- David Brody (@DavidBrodyCBN) August 19, 2020
The Pledge of Allegiance did not always contain the words "under God;" those words were not added until President Dwight D. Eisenhower signed it into law on June 14, 1954, 62 years after the pledge was first written by Francis J. Bellamy, in 1892. Over time, the Pledge of Allegiance had some changes to the words, as well as some major changes to how Americans are expected to salute the flag.
A nonpartisan review of the history of the changes to the Pledge of Allegiance and U.S. flag code is offered by Encyclopaedia Britannica's ProCon.org (here)(archived here).