In these examples that omit 'that' what is the distinction between those that can and examples that shouldn't.
I'd assume 1. is a comma splice as written, as their is a natural pause/break where the that should be, but 2 is a similar structure yet sounds ok.
1:The ice cream was so cold I had to stop eating it.
2:I am sorry I hurt your feelings.
panda blue 483 The ice cream was so cold I had to stop eating it. This is fine. ).
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panda blue 483The ice cream was so cold I had to stop eating it.
This is fine. "So" saves it from ever being a comma splice (The ice cream was cold, I had to stop eating it.). A "natural pause" is not the test for comma placement. Commas go where they are required and nowhere else in general writing. A comma would be wrong in this sentence.
panda blue 4831:The ice cream was so cold I had to stop eating it.
2:I am sorry I hurt your feelings.
Both sentences are OK. "that" is optional in both cases.
The numbering style is incorrect. At minimum you need a space after the colon, but I wouldn't use a colon. You can write it like this:
1. The ice cream was so cold I had to stop eatin
panda blue 483I'd assume 1. is a comma splice as written
The ice cream was so cold I had to stop eating it.
There is no comma in that sentence. Therefore it cannot possibly be an example of a comma splice.