Opposite words for rigidly:
loosely, imprecisely, inexactly.
Usage samples:
  1. It was not merely rigidly suppressed by the author, but immediately prior to publication it was destroyed by him, and, so far as I am aware, only one copy has, till now, been recovered.
    "The Book-Hunter at Home", P. B. M. Allan.
  2. I would rigidly counsel, one, and no more.
    "The Complete Project Gutenberg Works of George Meredith", George Meredith.
  3. I went, deliberately, holding my gaze rigidly to the front and using every ounce of self- control to curb the impulse of my feet to run, and the impulse of my neck to crane.
    "The Portal of Dreams", Charles Neville Buck.
  4. Her idle hands clasped themselves rigidly.
    "The Silver Horde", Rex Beach.