Modal must is used to expresses certainty, necessity, strong recommendation, and prohibition.
You must be a scientist. <certainty>
You musn't be late. <prohibition>
You mustn't drink tea. <strong recommendation>
You must drink tea. <necessity>
Now, to your examples:
1. He must be going to be late. <certainty>
2. He must be going to be a scientist. <certainty>
3. He must be going to drink tea. <certainty>
The pair must be going is grammatical; e.g. I noticed her bags are packed. She must be going to Iraq; however, with those constructs be going to takes a nominal, a location (i.e., be going to expresses movement, travel to a place), whereas with your examples, be going to expresses a plan of action.
The examples are meaningful, but awkward:
Example 3., the speaker is certain that the man plans to drink tea.
Example 2., the speaker is certain the man's plan is to be a scientist.
Example 1., the speaker is certain the man is going to be late.
The problem--if speakers do indeed see one--is in the opposition, and degree of compatibility, here: must (certainty) + be going to (plan). It expresses both certainty and uncertainty.
Does that help?