In my experience, putting tomato plants into one's compost pile would be OK IF the pile consistently heats up enough (above 130 degrees F) to kill all the seeds . . . which mine never does for long enough, and that is why I have been spending many hours on my hands and knees pulling 100s if not 1000s of tomato seedlings out of all the beds where I sprinkled my black gold earlier this year. I'm not going to put anything resembling a tomato into my compost after this season.
There has also been a thread anchored by Dr. Carolyn, the tomato-guru, about the fact that compost piles may not kill the fungal diseases that can afflict tomatoes and other veggies.
Fifty years gardening...49 years tomato vines went into my compost that rarely heated to the suggested 130 degrees...maybe never. The other year is this year's crops not adversly affected by the use of my compost. All spore of all fungi per any given geographical area are already in all of that area's soils and composts.
A ballanced good healthy soil will hold all matters and things in ballance yielding no problems of concern.
Please understand that an area with common deposit sites and compost grinding or mixing machinery accept all of the plant waste and all of it is used. That compost then is brought back to many yards and gardens. Do they do anything special? Absolutely not in fact management may be a little less than excellent. Given the proper time it all rots.
If your compost gets hot, it kills off the seeds, not a big deal. I just cut them up first to help them break down faster. I either turn the plants under or pull them up and shred for the bins. Just depends on how busy I am.