omitting the "that" in "the reason is that..."?

[MrPedantic]

Would I sound foreign if I keep using the present tense there, or do native speakers also often not follow this rule?

I wonder whether the question relates to these two variants:

1. "I gave you a ring yesterday. It's made of gold."
2. "I gave you the reason yesterday. It's that I was sick."

If so, #1 is fine. It does not sound "foreign". A ring is a long-term phenomenon; if it was made of gold yesterday, we can assume that it's still made of gold today.

#2 is also fine; for instance, the sentence might answer the question "Why are there no entries in your diary for 30th August?" (Answer: "I gave you the reason yesterday. It's that I was sick.")

Compare this sentence, which is also fine:

4. "Why didn't you phone me on the 30th August?" "I gave you the reason yesterday. It was that I was sick."

MrP