The opponents maintain that using HTTPS is obfuscating the app, that the app should behave transparently and send all the traffic over HTTP so they can see what they are sending, because the data is "anonymous" anyway.
I'm going to assume the boldfaced "they" refers to the end user, and not to the developers (because if it does refer to the developers, then this is a straightforward problem of not using appropriate debugging techniques such as server-side logging).
Realistically, how many of your end users are going to be running Wireshark or a similar piece of software? Of those that are technically proficient enough to run Wireshark, how many are seriously going to find HTTPS traffic suspicious? It's quite possibly the second most popular (layer 7) protocol in the world (after SMTP, I would tend to imagine), and as you say, the DP-3T protocol explicitly requires its use. Anyone who would find it suspicious is unlikely to know enough about networking technology to use Wireshark in the first place. In my opinion, the use of unsecured HTTP is more likely to provoke suspicion than the use of HTTPS.
On the other hand, it's quite possible to hide data in unencrypted network streams using any number of different forms of steganography (in this case, by hiding some data in the purportedly "random" ephemeral IDs that are used by DP-3T, and/or in the secret key when it gets uploaded for an infection report; both of those are opaque blobs of binary data with no meaningful structure for the user to introspect). So the fact that the technical end user is capable of monitoring your app's traffic doesn't actually help all that much with trust anyway.
In any event, we can clearly see that:
- This doesn't convince non-technical users of anything.
- It's unlikely to be effective in convincing technical users that your app is safe, and might convince them that your app is unsafe or at least poorly-designed.
- As described in multiple other answers, TLS does other things besides confidentiality, and that may compromise the security of your implementation in other ways.