Rambam was asked (Teshuvos Harambam 46) whether it’s right to stand for the reading of the Aseres Hadibros. Many have the custom to do so to remind us of the time we stood when we received the Torah. The Gemara (Berachos 12a) tells us that the Chachamim did not incorporate the Aseres Hadibros into the davening as there was a danger that some would think like the heretics that this was the only passage given at Sinai. Similarly, writes Rambam, one who normally sits during leining must not stand for the Aseres Hadibros.
While many acharonim including R’ Moshe Feinstein (Igros Moshe OC 4:22) and R’ Ephraim Greenblatt (Rivevos Ephraim 6:153:14) justify standing, R’ Ovadia Yosef (Yechaveh Da’as 1:29) writes that had they seen Rambam’s responsum they wouldn’t have written what they did.
R’ Moshe Sternbuch (Teshuvos V’hanhagos 1:144) recommends standing up before the Baal Koreh begins reading the Aseres Hadibros so no one will mistakenly think that the Torah is only comprised of the Aseres Hadibros. R’ Ovadia Yosef writes that as the Rabbi is usually honoured with this aliya it would be okay to stand for him and remain standing.Nonetheless, R’ Moshe writes that whatever one’s individual practice, one must join in with everyone else, and not go against the norm. While the individual may not have much choice, the tzibbur should either remain seated throughout, or stand for the whole aliya.