Hi tbox9, and welcome to the Apple (user-to-user) Community!
Re: Allowing accessibility to my computer to Dropbox?? Yay or Nay??
(1) I'm not sure what this means exactly
Am no expert in this area, yet your request certainly deserves some response.
Wondering if you use DropBox with other devices as well as for sending Photos from your Mac
Seems Apple provides AirDrop for sending items between Apple devices, like between iPhone and Mac.
Eg: See: Use AirDrop on iPhone to send items to nearby Apple devices - Apple Support
and
other ways to do the same transfer:
Transfer files wirelessly between your iPhone and computer with email, messages, or AirDrop - Apple Support
or transfer in the other direction:
Use AirDrop on your Mac to send files to devices near you - Apple Support
Info. about: AirDrop security - Apple Support
(1) Seems Dropbox may be asking if you also want DropBox to provide this service. I could be wrong.
A "Yay" may mean others can use DropBox to also send files to your computer ?
(2) Re: If I should or should not do it. "It makes me nervous to give any app access to my computer".
You may need to ask yourself whether you want to (a) allow others using DropBox to send files to your Mac:
and / or
(b) to transfer files between your own computer(s) and devices:
Seems this a personal choice of whether you use the AirDrop software Apple provides, or use a third-party
(non Apple) app. If you are concerned about privacy:
Eg: You can read about the DropBox privacy-handling of data
https://apps.apple.com/us/app/dropbox-cloud-photo-storage/id327630330
and
DropBox Developer's Privacy Policy: https://www.dropbox.com/privacy
Hope there's something useful to you here.
At the very least, discussion about your question is underway, allowing others to participate if they wish.
All the best :-)