I don't think the public would've reacted all that differently, some hard core fans may not have liked it, but that wouldn't last. However a year after The Voyage Home was released we would get The Next Generation, and a new Enterprise - I think that is when fans (and people in general, I suppose) got used to the idea of there being a new design and such. I suppose some people just wanted Kirk and Co. in familiar surroundings or something. But when TNG aired we found out there were two other Enterprises before the D came into service - so then the speculation began as to what class of starships they were, and I think fans eventually started enjoying the fact there were different Enterprises.