The main objective of this article, the first in a dedicated series, is to report basic results on systematic research of low-redshift optically selected SDSS Type 2 active galactic nuclei (AGNs) but with apparent optical variabilities. For all the pipeline-classified Type 2 AGNs in SDSS DR16 with z<0.3 and signal-to-noise ratio >10, long-term optical V-band light curves are collected from the Catalina Sky Survey. Through all light curves described by a damped random walk process with process parameters of {sigma}/(mag/days^0.5^) and {tau}/days, 156 Type 2 AGNs have apparent variabilities with process parameters at least 3 times larger than corresponding uncertainties and with ln({sigma}/(mag/days^0.5^)){>}-4, indicating central AGN activity regions directly in the line of sight, leading the 156 Type 2 AGNs as misclassified Type 2 AGNs. Furthermore, based on spectroscopic emission features around H{alpha}, 31 out of the 156 AGNs have broad H{alpha}, indicating the 31 Type 2 AGNs are actually Type 1.8 and/or 1.9 AGNs. Meanwhile, 14 out of the 156 AGNs have multiepoch SDSS spectra. After checking multiepoch spectra of the 14 objects, no clues for appearance and/or disappearance of broad lines indicates true Type 2 AGNs rather than changing-look AGNs are preferred in the collected Type 2 AGNs with long-term variabilities. Moreover, a small sample of Type 2 AGNs have long-term variabilities with features roughly described by theoretical tidal disruption events (TDEs) expected t^-5/3^, indicating probable central TDEs as further and strong evidence to support true Type 2 AGNs.