That’s the question posed by Joshua Douglas in this draft article, to be published in the Cornell Journal of Law & Public Policy. From the abstract:

The answer, surprisingly, is not always….
This article first identifies the inconsistent approaches to how the Court views the right to vote, with a detailed discussion of how Crawford adds to the jurisprudence. The article then attempts to locate a reconciling principle, but concludes that no one theory best explains all of the cases. After delineating the negative implications of this fractured methodology, the article proposes a two- part solution:
First, courts should distinguish between cases that directly impact voters from disputes involving indirect burdens. Regulations involving direct burdens on individuals – such as cases about the value of one’s vote or who is eligible for the franchise – impact the fundamental right to vote and deserve strict scrutiny review…. Second, courts should attenuate the approach to strict scrutiny for election law disputes, with an added focus on the narrowly tailored prong, so as to recognize the value of the right to vote while still allowing states to ensure fairness through their election regulations.