As stated in this question, coproducts commute with pullbacks in the category of sets.
Let $Grpd_{\infty}$ denote the $\infty$-category of $\infty$-groupoids. Do coproducts commute with pullbacks in $Grpd_{\infty}$?
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Yes, they do, if you mean what is meant in the question you linked, but it is misleading to describe this property as "coproducts commute with pullbacks", say instead "pullback along a fixed morphism preserves coproducts", or "pullback functors preserve coproducts", or with more jargon, "coproducts are universal".
More generally, colimits are universal and this is one of the defining properties of an $\infty$-topos. See the discussion in section 6.1 of Lurie's Higher Topos Theory, specifically proposition 6.1.3.10.
EDIT: Thanks to Marc Hoyois for pointing out an absent minded mistake in a previous version!
The thing I would call "coproducts commuting with pullbacks", is the following property: given diagrams $X_i \to Z_i \leftarrow Y_i$, the canonical morphism $\coprod_i X_i \times_{Z_i} Y_i \to (\coprod_i X_i) \times_{\coprod_i Z_i} \coprod_i Y_i$ is an isomorphism (or equivalence, if you prefer that term). This also holds in spaces and indeed in every $\infty$-topos. More generally, in $\infty$-toposes coproducts commute with limits over connected categories.
answered Jan 31, 2017 at 5:49
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3$\begingroup$ Coproducts do commute with pullbacks in any ∞-topos. In your example you forgot that the pullback is over $*\amalg *$. $\endgroup$ Jan 31, 2017 at 8:40
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$\begingroup$ That was careless of me. Thanks for pointing it out, @MarcHoyois. $\endgroup$ Jan 31, 2017 at 9:41