To be honest, I've never tried to use an SVG for an avatar. Did you receive some kind of error message? I'll try....
The error message is "The avatar you have selected is either too large or not an avatar."
By that language "not an avatar" gives me the idea that SMF software uses some kind of definition for what an avatar is. I have no idea what that might be, but I'd be glad to look into it via SMF support, if you're interested.
The options which the SMF software provides for avatars include dimensions of an image, but it doesn't mention file size. It doesn't mention file type (mime type) either. I'll try something else. First (where I got that error message) I tried uploading an SVG avatar. But this time, I'll try putting an SVG avatar into the cache of avatars which we provide for users to choose from (if they don't want to upload their own).
So far, so good. It wasn't rejected when I uploaded to the av directory. Ah, but in the end, it doesn't show up in the list of available avs.
I'm guessing that there is some limitation where only PNG, GIF, and JPG are allowed for avatars. I'd be glad to try and find out more about it, if you're interested. But this is something that's controlled by the SMF software, which I can't control. (Well at least not yet. There's a chance if I ask for support, I'll learn some way to make it possible. But probably a tiny chance.)
One way in which this forum is progressive about using SVG images, which no other forum software provides (at least that I know of), is that if you upload an SVG attachment, it's actually displayed as an image, instead of just a download link. That became possible because I provided feedback to the author of one of our attachment mods.
If we were to stumble across the right programmer, we might be able to convince them to make SVGs possible as avs. But I'm not sure having SVG avatars would do much to promote the advancement of SVG as an image format. However, please feel free to try to convince me otherwise