I committed the new versions of the adobe htf files to TeX Live (r51905).

I also realized that a number of htf files were being generated in tex4ht dev but weren't in TL yet, so I committed those too (r51906).

Finally, I noticed that three files in TL were no longer being generated (as far as I could see), so I removed them:
unicode/ec/eccc.htf
unicode/pxfonts/pxbsyc.htf
unicode/txfonts/t1x.htf
(in texmf-dist/tex4ht/ht-fonts). Guess we'll see if that causes trouble.

More discrepancies remain between dev and tl, but we'll resolve those another time. Closing this ...

The following input:

\documentclass{article}
\usepackage{avant}
\usepackage[T1]{fontenc}
\begin{document}
first
\textsf{first}
\end{document}

with the following command:

mk4ht htlatex a.tex "html,uni-html4,css2,charset=utf-8,info" " -cunihtf -utf8"

gets the following HTML output:

first
ørst

Notice how the fi (fi; U+FB01) ligature becomes ø (small o stroke; U+00F8).

Further please note that when selecting another font the problem disappears. The original reporter listed the font families below.

These fonts work:
- computer modern (default)
- lmodern
- charter
- palatino
- times (both serif and sans-serif)
- utopia

These do not:
- avant
- bookman (both serif and sans-serif broken)
- chancery
- newcent (both serif and sans-serif)