Be warned this a personal point of view as of the situation on 3 January 2014!
Is travelling to Thailand safe?
As said the protest are mainly (98%) in Bangkok city. And mainly in the center of Bangkok. So, yes travelling to Thailand is safe. You will arrive at the airport and from there you will continue to your destination like Chiang Mai, Phuket, Koh Samui or Pattaya. So I would say "Yes, traveling & staying in Thailand is safe".
But is travelling & staying in Bangkok safe?
There are millions of people living in Bangkok and 99.99% of them are not less safe due to the protests. Travelling in Bangkok might be a bit more problematic as it always has been. Like going from the airport to the train-station to go to Chiang Mai. Or like going to tourist attractions might be a bit more problematic as it has always been. So I would say "Yes, travelling & staying in Bangkok is safe, as long as you stay out of the protest zone's".
Advice for travelling in Bangkok:
- More people will use BTS & MRT so it will crowded
- Due to the planned "grid-lock protest" traffic might be jammed like it is 1990 again
- Due to extra traffic jams there might be less taxis at the airport
- Stay out of the protest zones
- Keep yourself update about what is happening