I have been on Mounjaro for 10 months and have lost 7st.
When I started I had been prescribed daily omeprazole for acid reflux for 7-8 years. I couldn't go a day without taking it without being very uncomfortable.
4-5 months into Mounjaro after about 3-4st loss I tentatively stopped and haven't taken since. Obviously that is only anecdotal, for many people it does cause GI issues and/or worsen symptoms, you won't know until you try.
With existing acid reflux try to work with Mounjaro by having smaller meals, avoid late meals, chew slowly, avoid trigger foods (for some that is fatty, spicy, fizzy, citrus, acidic foods such as tomatoes etc), drink plenty of water, etc. I think Mounjaro changing and simplifying what I wanted to eat has removed triggers, and of course the weight loss will have helped too.
As a watch out, lots of people on Mounjaro, especially facebook groups, recommend peppermint oil capsules for any GI issue. Be careful if you take them with acid reflux especially if using antacids too. The antacids can cause the peppermint oil capsule coating to dissolve in the stomach rather than where they should in the intestines. The peppermint oil then relaxes the sphincter muscle which should keep acid in the stomach, making it easier for the acid to escape leading to worsening acid reflux.