I'm going to answer this to cover two aspects - social media accounts for visas, and social media access AT the border, since they're related and will probably be asked as well.
Currently for some visas, you're now asked for your social media accounts as a foreign traveller to the US.
The US government has begun asking select foreign travelers to
disclose their social media activities as part of an expanded effort
to spot potential terrorist threats.
The request functions as a prompt on the online Electronic System for
Travel Authorization, or Esta, a visa waiver application that many
visitors are required to submit before travelling to the US. The
choices include platforms such as Facebook, Twitter, Google+,
Instagram, LinkedIn and YouTube, and additional space for applicants
to input their account names on those sites.
However, obviously not every person has a social media account (including members of my family).
The CBP has stated:
it wouldn’t prohibit entry to foreigners who didn’t provide their
social media account information.
It's a weird request. In theory if they find someone suspicious, they could use their social media to look up more info about them. Equally, it could help clear them. However, much like some of the other questions (are you a member of a terrorist organisation), it's unlikely any 'problem person' is going to volunteer their social media accounts. However, others feel insecure if they don't complete a full visa application, and the information may be used for other things, like cross referencing with other govt organisations wondering who the followers of x are, or who is tweeting from y.
However, that's speculation. The key answer to your question, again - for now, is:
it wouldn’t prohibit entry to foreigners who didn’t provide their social media account information.
Similarly, if they ask you for your actual login credentials (eg password), and you say you don't have one, it can't be held against you. However, if YOU did have one and said you didn't, and it was later found to be a lie, then you've lied to a government official, and THAT can be held against you.