String of jumbled text is appended to every incoming SMS with Project Fi

It looks like there's something wrong in your carrier's SMS router. You should contact your carrier and ask for support.

There's no encoding issues in this case, so I disagree with @beeshyams . The appended text is a stream of base64-encoded data, which after being decoded, resembles a stream of 11-byte data. According to my experience, it is very likely some metadata of the SMS message you received. You can safely ignore it.

Edit: Merged information from comments.

This is a general phenomenon of using Project Fi's service on a non-Fi phone. Discussions are here and here. A solution is to use Google Hangouts for text messaging.

Appendix: Decoded info from image (re-formatted manually)

$ base64 -d | hexdump -Cv

q/Pj/QAHwY+Jhgg= : AB F3 E3 FD 00 07 C1 8F 89 86 08

jaT2JQAcd3EM7Ag= : 8D A4 F6 25 00 1C 77 71 0C EC 08

BMXciQANmWXBLQg= : 04 C5 DC 89 00 0D 99 65 C1 2D 08