With many conservatives and Donald Trump backers in a lather over heightened scrutiny of Facebook and Twitter posts during election season, social media startup Parler is emerging as a fast-growing alternative.

The Henderson, Nv-based company, founded in 2018 by computer programmers John Matze and Jared Thomson, says its membership swelled to about 8 million from 4.5 million in just the past week. Parler’s app is the No. 1 download in the Apple iOS and Android stores, according to measurement firm Sensor Tower. Other social media players like Gab or MeWe have similarly benefited from conservative angst about Silicon Valley’s so-called “censorship,” but Parler’s gains have been the most significant of any alternative outlet to date.

Joe Biden’s defeat of Trump in the 2020 presidential election was confirmed by major media outlets Saturday but has not been widely accepted by the Republican establishment. Members of the administration and Congress continue to insist...