Are there any homomorphic first and second preimage resistant (cryptographic) hash functions? Are there any homomorphic cryptographic hash functions that satisfy $\text{H(A + B)} = \text{H(A)} + \text{H(B)}$ which maintaining pre-image resistance
Fix a finite group $G$ of order $\ell$, written additively, in which discrete logarithms are difficult.  Fix a standard base point $P \in G$ of large prime order.  The function $H\colon \mathbb Z/\ell \mathbb Z \to G$ given by $$H(n) := [n]P = \underbrace{P + \cdots + P}_{\text{$n$ times}}$$ is a preimage-resistant homomorphism: $H(n + m) = H(n) + H(m)$, and finding preimages is exactly finding discrete logarithms.

Of course, if $\ell$ is prime, then $H$ is injective and so doesn't compress its input at all; while if $\ell$ is composite, then $H$ is not collision-resistant since $H(n + \operatorname{ord} P) = H(n)$ for all $n$.  See the linked answers to address collision resistance.