Is Houdini 6 a Stockfish clone? I've been hearing this claim being bandied about quite a lot and I'm wondering if there's any substance to it. Apparently the details are in a certain thread on Talkchess, but it's not viewable to non-logged in readers, and it won't let me register. There are no details about this on the Houdini Wikipedia page either.

Can anyone give a summary of the allegations and the evidence for (and against) it?
Yes. 

The search, evaluation, etc., are almost identical to Stockfish, with the notable exception of being rewritten in Dutch. A number of Stockfish developers, including former maintainers, have noted as such. To hide its origins, code was included that multiplied the node count by 8/7. Exploiting modular arithmetic tricks and archived Houdini games, this exact code was shown to be present in the release version of Houdini. The alleged performance improvements over Stockfish go away after removing this trick.

The leaked source code was compiled by Ed Schroder and found to have a 1:1 correspondence with Houdini in a vast number of test positions, while others, like Simon Guenther, have found that the leaked code behaves identically in the start position even up to high depths. 

There were changes, but Mark Lefler, developer of Komodo, noted that a number ofaa changes were simply adding features reverse engineered from Komodo. In fact, in one file, evaluatie.cpp, you can spot the naming conventions used by the Hex-Rays decompiler.

Other features were unique, but minor. For example, the licensing system was not from Stockfish. However, the code came from TurboPack and was translated into C++, so it's not clear that that was original work, either.

Adjusting for the time of release, the version of Stockfish on GitHub at the time of Houdini  5's release was more or less equal in strength to Houdini 5. Later, when Houdini 6 was released, this was also true. (Source: nextchessmove's elo data + CCRL data)

In other words, Houdini did not notably build upon Stockfish in any meaningful way. The main reason it looks different is because of the Dutch translation and the fact that Stockfish has evolved significantly since Houdart last touched the Stockfish codebase.