Can universal hashing functions be (ab)used as stream ciphers? These days, universal hashing functions like GHASH and Poly1305 are very trendy because of their simplicity and speed.

Now during a discussion related to export restrictions, it came up that mainly encryption techniques are regulated and these hashing functions wouldn't be hit by this.

Now to the question:
Can you run a universal hashing function in CTR mode to get a secure stream cipher?
No. Consider the simple universal hash function $H(k, x) = k \cdot x \in \mathbb{F}_{2^n}$. It is universal as $\text{Pr}[H(k, x) = H(k, y)] \le 1/(2^n - 1)$ for a randomly-selected $k$; polynomial evaluation degenerates to this function when run on a single block. If you run this in counter mode you get as ciphertext $k \cdot 0$, $k \cdot 1$, $\ldots$, which is clearly insecure and leads to immediate key recovery.

Universal hash functions (or the weaker almost-xor-universal variants) work with authentication because their sole job is to uniformly map a potentially long message to a shorter one; the secrecy job is handled by some PRF or PRP.