For the Normal Distribution, why is the case that "<" (less than) is the same thing as "<=" (less than or equal to), computationally? That is, why can we summarily disregard the "equality" portion?

It's not just the normal distribution - it's true for any continuous distribution. The reason is because the probability of observing a specific value is 0. Symbolically if \(X \sim N(\mu, \sigma)\) then \(P(X = x) = 0 \hspace{.2cm} \forall x \in \mathbb{R}\)