How do you transfer photos from Mac to thumb drive?

Drag and drop works just fine for me.

Select them all and use the File->export facility. You can choose to export the unmodified original files or JPEG copies which will honor any edits.

Export them to a folder on the desktop - I have a permanent "exports" folder there and then copy that to your USB drive. (The two step process is due to an overabundance of caution, at some point in the past saving directly to a USB drive failed.) Note that some FAT formats on the USB stick limited the number of files in the root of the drive, so it might be best to drag the whole folder as opposed to just the images.

Are you using DAM software like Photos?

Are you trying to transfer a few photos or a whole library?