I checked my DNS logs and saw zero attempts to resolve `log.tailscale.com` having ran tailscale for many years (I added it to a blocklist anyway). From their admin panel, it appears "networking logging" requires paying for Premium[0], so it's not being used for free users (or Personal Pro).
Also, from looking at some source code (because the docs don't include this), I discovered you can disable logging for the macOS App Store client by doing:
echo "TS_NO_LOGS_NO_SUPPORT=true" > ~/Library/Containers/io.tailscale.ipn.macos.network-extension/Data/tailscaled-env.txt
[0]: https://login.tailscale.com/admin/logs/networkI highly doubt any of this can actually be opted-out of. How else would they stay in business?
The core client code is open source, feel free to inspect it yourself.
Don't let that deter you from trusting whomever you choose, though.