Does taking synthroid (thyroxine) affect osteoporosis?

No: It will not cause or affect osteoporosis unless you take too much and became hyperthyroid.

Maybe but it depends: If taken as directed w/regular monitoring to keep you in the "normal" reference range, synthroid or any other brand of generic levothyroxine should not affect your bones and cause osteoporosis. However, if taken in excess w/resultant suppression of TSH (leading to inadvertent hyperthyroidism), then yes, too much synthroid can increase bone turnover causing osteoporosis.