Lets get some things clear
1. If you are anything other than a UK or Irish national you need a passport or national ID card
2. Everyone arriving in Dublin Airport will go through immigration, no passport = no entry unless you have a Irish or UK drivers licence which shows you to be Irish or UK national and arrived on a UK flight
3. They do check the trains and buses on a regular basis, not as often as before but it does happen
4. Travelling Ireland -> UK you go through the domestic channel and bypass all immigration though legally a non UK/Irish national should report to the immigration service at that airport