Is it grammatically correct to say, "It's so fun."
Well, in fact, I think it is. At least in the US. Maybe a little bit informal.
Fun has more than a century of use as an adjective and is used as one on this site in at least a couple places:
Making textbook listenings manageable and fun - Teacher Articles - UsingEnglish.com
Learning Vocabulary Can Be Fun - ESL Web Directory - UsingEnglish.com
Fun - Definition and More from the Free Merriam-Webster Dictionary
Main Entry: 3fun
Inflected Form(s): sometimes funĚner; sometimes funĚnest
Date: circa 1846
1 : providing entertainment, amusement, or enjoyment <a fun party> <a fun person to be with>
2 : full of fun : pleasant <have a fun time>
And yet, there are traditionalists, who may include your teacher, who will tell you that it is a noun and can only function as a noun. So know your audience.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
*** I'M NOT A TEACHER ***
It brought a scene from one of my favourite movies, "Cold Comfort Farm", to my mind:
- Oh, it's going to be such fun.
- No, it's going to be ''amusing'' or ''diverting,'' not ''such fun,'' darling.
Yes, it is grammatically correct.
(Although I don't like it much and don't like to use it.)
Fun and funny are adjectives.
(Fun is also a noun.)
Funny can be used if you laugh about someone.
You're so funny (ridiculous).
However, I don't think anyone would misunderstand "It's so funny."
**Neither a teacher nor a native speaker.**
Whether some dictionaries grant the word adjective status or not, the majority of speakers do not consider 'fun' suitable for formal use as a true adjective (i.e. as a word that can be modified by an adverb such as 'very' or 'so'). However, that does not rule out entirely its use as an attributive noun, permitting its combination with other nouns, as in
a fun episode
, or, of course, its use as a complement, as in
That was fun.
In formal/careful usage, any intensification of the word as a complement will be accomplished by means of adjectives rather than adverbs. Hence
That was great/such fun.
?That was very/so fun.
No. But unfortunately, sometimes popular usage rules and you hear the expression especially among the youth of the day.