Yes, unfortunately we have the deuteranopia theme, but that neglects the log file (and red text in other parts of the GUI). I've filed an enhancement request and I hope we'll improve that soon.
In the meantime, the log does get written to a file, so there's no need to copy and paste. You can just open the log file in Notepad++ with colors turned off. Or you could even set up a special color/syntax highlighting for FME log files in Notepad++ that uses a different color to red.
I've also asked the question on the FME knowledge centre. I figure a temporary solution would be a Python shutdown script that extracts log error messages and presents them in a different way - or even just pops up a dialog saying "there was an error".
Would that help? Sadly my Python skills are fairly poor, but I'm sure someone either here or in the FME community would be able to come up with something good.