Which are both silly reasons really. The looks of the aliens in Star Trek have always been updated. Klingons, Romulans, Trills, Borg.... It's not a valid reason, it's a childish complaint. When TMP was first released, fans had the same silly outcry. No one cares anymore.
As for the way the rest looks..... TOS was made with effects and technology of that time. Discovery is made with those of this time. If the show was made to look exactly like TOS, this forum would have gone nuclear already from all the complaints.
And as for all of this Prime versus Kelvin versus whatever..... It's Prime. Not because of what I think or feel or might desperatly need to satisfy my inner geek. No. Simply because the creators of the show clearly stated it's set in the Prime Universe. You can close your eyes and ears and go 'LALALALALALALALALALALA' as loud as you want and ignore it, but that's not gonna change it.