What are the benefits of being social?

They will give you recipes and, very occasionally, small gifts via mail.

Being a game where you do the things that you want to do though, if making friends isn't what you want to do, don't do it.

However, arguably the most important thing that making friends does is it gives…

The game's story

Being a farming RPG, arguably just making friends is part of the benefit. There is a story (more story than “plot” since it's not linear) to Stardew Valley, and it's revealed by getting to know the NPCs.

Not making friends is like running around in Skyrim without ever doing the main quest: totally doable and it can be lots of fun and entirely fulfilling for a given player, but from an objective measure it results in missing a significant percentage of the game's content. (No backhanded criticism is implied here! This is how I personally play Elder Scrolls games.)

But again, this is a matter of taste. Getting to know the NPCs can be fulfilling in the same way that playing To The Moon is. But for those who like the Tycoon-game aspects of Stardew Valley more than the To The Moon aspects, the game is clever in allowing the player to find and focus on the things they personally find interesting. As one review put it:

The flexibility and freedom in Stardew Valley is without a doubt its greatest strength. It is one of those games that gives you so much autonomy that it ends up becoming more of a roleplaying game than anything else. Your avatar in the game adopts a personality through your actions. Are they helpful and neighbourly? Are they looking for love? Or are they driven to explore the many mysteries of the village? Worryingly, my character seemed to have become a paranoid recluse, scuttling into town only briefly to buy seeds before returning to his ramshackle farmhouse, his dog and his ever expanding patch of parsnips.

Other than the spouse, friends will gift you items and recipes through the mail, plus some will trigger "events" at certain affection levels, if that is of any interest to you. There are also several achievements related to having certain relationship levels with one person or more.

None of it is mandatory of course, and you can choose to ignore it altogether.

I should add that being social really doesn't necessarily cost you money, I've raised Linus' affection to 10 by early winter by gifting him nothing but Berries found in bushes that sell for scraps anyway and he's given me several recipes and items in return. Many people are happy with very cheap gifts, especially if you give it to them on their birthdays. Plus, just talking to people actually raises their affection some.

As others have said, but to add a few
a.) Achievements
b.) Gifts (in the mail, etc.)
c.) Cutscenes
d.) Role playing (digital girlfriend)

A warm fuzzy felling inside?

The social aspect doesn't really give you considerable perks or anything for your farm, it is there mostly to give you that sensation of living on a small town where everyone knows each other, plus, it triggers some cutscenes.

And to be fair, I just reached summer, and even though I used a part of almost every day to go and socialize (including gifting to multiple people), I still had enough resources to get a silo, some tappers, a pair of bee houses, two copper tools and a coop is on its way.