A lot of people like to tell you whether you "should watch" something. Obviously, there's a little arrogance at work there—like you're not a "real" fan unless you've seen this—but I want to approach this question from a different angle: is Neon Genesis Evangelion important enough to watch?
Evangelion is one of the most talked about, most controversial, most beloved and most eyes-rolled-at anime ever made. Its characters remain a regular fixture of cosplay at anime conventions and show up in fanart even today. They're even making new entries in the franchise 25 years later with the Rebuild movies.
So this is not a question of whether this show is "good" or not, whatever the heck "good" means when appraising art. Is Evangelion enough of a cultural touchstone that watching it will improve your conversations with others about anime?
To answer this question, let's go back to the original release of Evangelion, both in Japan and America.
In Japan, Eva was a mega-hit, popular even beyond the sizable market of hardcore otaku at the time. This is remarkable because Eva is clearly aimed pretty squarely at otaku: it takes common mecha tropes and twists them in surprising ways, and many of its elements are homages to fan favorites like Ultraman and Godzilla. But that's another video.
Point being, in Japan, everyone watched Eva, so it became a cultural touchstone in Japan. An average Japanese middle-aged housewife would recognize an image of Asuka, even if she couldn't immediately name her.
Further, the finale of the TV series enraged otaku in Japan, causing intense debate and discussion. The later movie entries ramped up this controversy.
So if you're a Japanese fan, yes, there's enough history behind Evangelion that it's worth familiarizing yourself with it.
But if you're watching this you're probably not Japanese—at least according to my stats—so why should it matter to you?
When Evangelion was finally released in North America, fans in the west had already heard about it. Some had even found laserdiscs and fan translations. So Evangelion had a reputation.
As a result, Eva hit the West like a runaway freight train. Not only were knowledgeable fans recommending it, a lot of viewering went into it knowing it had its issues, and were thus a little more forgiving (er, fandom was different back then).
Further, Western fans were much more familiar with the Judeo-Christian symbolism that Hideaki Anno slathered all over Evangelion like a 5-year-old icing her own cupcake. Remember, most Japanese people have only vaguely heard of the concept of the three Magi. To Westerners, this was an anime actually incorporating Judeo-Christian elements into its storyline, and so the theories and discussion multiplied.
Further, while Evangelion is by no means a tightly integrated set of storylines and themes woven into a perfectly aligned tapestry that resolves every plot thread in the end, it's also not a generic action series. There is consistent symbolism here, and multi-dimensional characters, and an ever-developing plot.
So, for all these reasons—look, I'm not going to tell you that you have to watch Evangelion. It took me years to finally get around to it. But I will say this: watching Evangelion will definitely give you something to talk about.