Evidence-graded answer
Is GLP-1 safe to take with thyroid medication?
Yes. GLP-1 medications do not interact with levothyroxine or other thyroid hormones. Take levothyroxine on its usual empty-stomach schedule (30-60 min before food); GLP-1 has no effect on its absorption.
Personal/family history of medullary thyroid carcinoma (MTC) or MEN-2 is the only thyroid-related contraindication — and that is about MTC, not about taking levothyroxine.
Levothyroxine should be taken on an empty stomach with water; GLP-1 timing is independent and flexible.
Periodic TSH monitoring is reasonable for anyone on GLP-1 + thyroid meds, especially during weight loss (TSH dose requirements sometimes change).