I don't really hate wine, but I'm not that big a fan either.
I don't dislike wine, but I'm not what you call a wine lover either.
この場合、次のような言い方ができますよ。
ーI don't really hate wine, but I'm not that big a fan either.
「ワインは嫌いじゃないけど、そんなに好きでもない」=「少し苦手」
I don't really hate ..., but I'm not that big a fan either. を使って言えます。
ーI don't dislike wine, but I'm not what you call a wine lover either.
「ワインは嫌いじゃないが、ワイン愛好家でもない」
I don't dislike ..., but I'm not what you call a wine lover either. のようにも言えます。
ご参考まで!