Is there a problem with wearing sandals or Crocs during Davening instead of regular footwear? What is the source for this issue and what is the reason for this issue?
The halachic gauge for how to dress for Hashem is how people dress in front of "great people" and every place is different (Shulchan Aruch O.C. 91:5 MB 12-13). I assume that Israel has a more laid back standard than, say, the U.S. In Israel, people might visit the Head of State in sandalim.
This opens a big can of worms. Can a person wear jeans and a polo shirt? Unpressed slacks? No tie? Scuffed shoes?