Continuous-variable (CV) cluster states offer a promising platform for large-scale measurement-based quantum computation (MBQC), but finite squeezing inevitably introduces Gaussian noise. Since scalable non-Gaussian resources for fault tolerance remain experimentally challenging, a central question is how this accumulated noise constrains near-term computational power. We address this question by analyzing the classical complexity of measurement-based linear optics (MBLO). For every gate setting in our explicit MBLO framework, we establish nonasymptotic squeezing bounds for both exact and approximate classical simulation, showing that fixed squeezing eventually leads to classical simulability. Conversely, increasing the squeezing sufficiently with system size supports provably hard regimes under standard complexity assumptions, thereby revealing a squeezing-driven complexity transition. We further determine how homodyne inefficiency expands the certified-easiness regime while contracting the provable-hardness regime. Finally, we numerically characterize the entanglement properties of the output states and observe a related finite-size entanglement crossover, providing a complementary physical perspective on the same noise-driven transition. These results help quantify how finite experimental resources constrain access to computationally nontrivial regimes as CV cluster-state platforms scale, and characterize the corresponding quantum-to-classical computational boundary.