Is it still the prevailing thinking out there that we should burn our spent tomato plants? Is it okay to put rotting tomatoes in the compost pile?
"Prevailing"? I don't know about that. It is debated true, but lots of tomato plants are composted each year by home gardeners with no problems. It depends in great part on your method of composting and if the plants are diseased or not.
Active, hot, well maintained and carbon-nitrogen balanced compost piles can cope well with just about anything, even diseased plants. So in that case the choice is yours.
With cold, passive, seldom maintained piles one should probably avoid adding any diseased plants since the beneficial bacteria and soil web will be slow to cope with pathogens and slow to decompose the woody material in plant stems.
Tomatoes themselves pose no problems. In an active pile they are quickly gone and most seeds are cooked. In a passive pile they can attract varmints and you'll get more volunteer sprouts in the spring.
You can read more about all this over on the Composting forum here.
I NEVER put the old plants in the compost because of the possibility of disease. I also NEVER put tomatoes in the compost to avoid volunteers.