Here is an MWE:
\documentclass[a4paper,11pt]{article}
\usepackage{polyglossia}
\usepackage[normalem]{ulem}
\defaultfontfeatures{Ligatures=TeX}
\setmainlanguage{magyar}
\usepackage{color}
\usepackage{soul}
\begin{document}
árvíztűrő tükörfórógép
ÁRVÍZTŰRŐ TÜKÖRFÚRÓGÉP
\hl{árvíztűrő tükörfórógép}
\hl{ÁRVÍZTŰRŐ TÜKÖRFÚRÓGÉP}
\end{document}
Here are some interesting message from the log:
Missing character: There is no ű in font ectt1000!
Missing character: There is no ő in font ectt1000!
Missing character: There is no ű in font ectt1000!
Missing character: There is no Ű in font ectt1000!
Missing character: There is no Ő in font ectt1000!
Missing character: There is no Ű in font ectt1000!
I'm not sure why it is complaining about font ectt1000. It can be seen clearly that the highlighted text and the normal text use the very same font. I do not see any error messages in the log. (Nor warnings - but this kind of misrendering should definitely throw an error!)
Here is the output:


ectt1000comes from\newfont\SOUL@tt{ectt1000}which is hard-coded insoul.sty. I tried\def\SOUL@tt{\ttfamily}or even\newfont\SOUL@tt{"[lmmono10-regular]" at 10.95pt }but then we get "reconstruction failed" although\SOUL@tt őűhas no issue and does work. (It appears the ecmtt font is used for inner constructs by souls when it typesets things in a box with 1sp width to force break into character per character for later reconstruction; but how this come into play when the final output does not use tt font, I forgot) – Nov 16 '16 at 08:24soulpackage typesets your text in a very narrow box with the fontectt1000in order to split it up in syllables. It uses attfont to prevent ligatures to be made. It seemssoulis not compatible withfontspecbased typesetting. It seems to need the older TeX font system. Maybe you should report this as a bug. – Pieter van Oostrum Nov 16 '16 at 09:08