Is it okay to write this:
Her condition was that he should not be allowed into her house.
Or, is the grammatical format this:
Her condition was that he not be allowed into her house.
If the context of the question is that she is making a demand, as in
A condition of the agreement is that he not be allowed within 150 feet of the house.
then the subjunctive is fine. It is more formal than the modal "should not be", however, if the context demands formality (as an agreement would), the subjunctive is not dated or old-fashioned but quite common.
Both are correct. The second example is in the present subjunctive and is more formal, but both are grammatically correct. I like the subjunctive form you give though and I would probably use it most of the time; however that's just my choice.