The correct option is
D P-S-R-T-Q
The sequence, 'People (P) who act in (S) public (R) should (T) stay at home (Q)', is complete, grammatically correct and forms a meaningful sentence. Hence, option A is correct.
Option B: The beginning sequence, 'People (P) who act in (S) stay at home (Q)', is grammatically incorrect and conveys no meaning. This is because part S (who act in) should be followed by a noun or a noun phrase. Hence, this option is incorrect.
Option C: The beginning sequence, 'People (P) stay at home (Q) public (R)', is grammatically incorrect and does not convey any meaning. Hence, this option is incorrect.
Option D: The beginning sequence, 'People (P) should (T) stay at home (Q) public (R)', is grammatically incorrect. There is no conjunction linking the two phrases, 'stay at home' and 'public'. Hence, this beginning sequence does not convey any meaning. Hence, this option is incorrect.