Absolutely not! Sure I may draw a line every now and then in terms of graphics but I've had many experiences where 'bad graphics' stopped being a concern when I found myself really enjoying either the story or the gameplay. Some people say the best game has the best of both. That may be true but come on guys, such ideal games don't come around every often. You might miss out on a lot of fun for the time being if you have too high standards in terms of graphics IMO.
Well, it depends what you mean by graphics. If you are generally talking about the graphics and geometrics of a game, then yes. There is nothing worse than an ugly looking game where objects don't seem to 'fit' are the layout/background hasn't been thought out and executed properly.
However, if you are talking about 'realistic graphics' then no. In my opinion, some games are better suited to look 'cartoony', or not as realistic. Zelda, Mario or other similar games would look absolutely ridiculous if they were moulded to realistic ideas. However, less realistic graphics would take away from the gaming experience of games such as Skyrim, CoD, and FIFA.
Ultimately there is no answer to this question, as it depends on what you classify graphics as and what game it is.
I'd also like to say that everyone going crazy and saying they 'hate people like that' or 'think that person is stupid' are taking this far too seriously. It's a matter of opinion and, like you get annoyed when these people discard your views immediately, calling them imbeciles for their matter of opinion is equally wrong.
I like graphics to be good in a game but it's not my main focus.
I like games with cute animals, decent game play, some kind of story or platline helps in some games.
For Animal Crossing, I got it as a down time game.
Meaning I play it to relax.
