What effect will the new US anti-encryption laws going to have on FLOSS?

Software source code is expressive. Yes, it is functional, but so much more than mere functionality is contained within: ideas about representing, abstracting, encoding, and solving problems (i.e. math); design patterns; pedagogical content (not just the functional code itself, but the source comments, specifications, manuals, etc.); idiosyncratic and often humorous bits--often part of or intrinsically linked to the code itself--that are expressions of emotion intended for human readers. Separating the functional from the non-functional bits as a test of expressiveness is a nonstarter. The two are often inseparable in the whole of the authors' expression.

All this is to say that Congress probably needs to meet strict scrutiny in order to prohibit the free communication of software source code. However, Congress does have a clear authority to regulate (nominally interstate) commerce. Prohibitions on the sale of software or devices with certain functionality might be kosher, but as I understand it, prohibitions on the distribution of software source code would face a much higher legal bar.

The compelled inclusion of backdoors in code you publish is unlikely to be Constitutional. Even if it did somehow become effective law, that would simply drive FLOSS developers underground. And like you say, code can be audited, projects can be forked, and the existing body of FLOSS software won't disappear overnight.

(IANAL)

A lot of good software business will move to the EU in my opinion the next four years.