Diagnosed with Hashimoto's 1.5 years after getting breast implants. Should I take my implants out?

Any foreign substance in the body can cause an autoimmune reaction, including breast implants. Though not well documented, breast implants have been thought to exacerbate existing Hashimoto's, so discuss the pros and cons with your PS.
The FDA says anyone with an Allergan BIOCELL textured implants should NOT have them removed, unless symptoms (persistent swelling or pain near the implant) are present. Should cancer occur, it is limited to the scar tissue and fluid near the implant, but it can spread through the body. While the diagnosis is serious and can lead to death, the risk is considered to be low.

You can choose to remove your implants at any time.  There is no recommendation to remove them unless you are having issues.  It is unlikely that they contributed to your Hashimoto's diagnosis, but if you are nervous you can elect to have them removed.

First, you need to be checked for food allergies, be very careful of what personal care products you use, and go organic with everything including clothing and sheets. Daily we deal with numerous chemicals, especially pesticides, which can cause autoimmune disorders. Second, not everything you read on the Internet is truthful, and many well meaning people are not well educated on facts. No, the implants do not hide cancer, especially breast cancer. Your breasts are in front of your implants. Third, discuss your concerns with your implants with your surgeon.