The one thing we didn't do was rush into anything serious.
I understand, I think, why it would seem more logical to continue with the past tense, but if you break it down like this:
"There was one thing we didn't do."
"What didn't you do"
"We didn't rush into anything serious"
...then perhaps you can see how it works. I'm afraid I know nothing about cleft or pseudo-cleft sentences, but "didn't rush" is the relevant verb here, and is the correct negative past tense.
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