Do I need a reentry permit for border trips with a METV visa in Thailand?

That is a 6 month multi-entry tourist visa <- meaning you can enter thailand an unlimited number of times during the validity of the visa itself (6 months from the date it was issued) and each entry will get you stamped in for 60 days

𝗗𝗼 𝗜 𝗻𝗲𝗲𝗱 𝗮 𝗥𝗲𝗲𝗻𝘁𝗿𝘆-𝗽𝗲𝗿𝗺𝗶𝘁 𝗳𝗼𝗿 𝘁𝗵𝗲𝘀𝗲 "𝗯𝗼𝗿𝗱𝗲𝗿𝘁𝗿𝗶𝗽𝘀?"

You're answering the question yourself, the METV is a MULTI-ENTRY tourist visa, the unlimited re-entry is built into the visa.

Look at the PDF that is your visa (which you should have printed out) across from No. of Entries it should say Multiple 🙂

That means unlimited entry & no re-entry permit needed. (y)

Also remember you can get one 30 day extension on each of those 60 day entries at the immigration office where you stay for 1900baht if you wanted to

Safe travels