Serious danger? Your privacy is pretty much nonexistent when you closed-source wallet, since you're connected to their server and it's likely they log everything (where there's no way to prove it's true or false).
But Coinomi does allow you to change the server it talks to (on the mobile version). Don't trust them for privacy, use your own server.
You can actually install a sniffer on your Wi-Fi and see that yes, once you change it it never talks back to them. On mine it has not pinged back for months except for update checks.
With others, like mycelium, their servers are hard coded in. Can't be changed without recompiling it yourself.
And it also goes back to something I posted last year in this thread and in many other places:
If you have life changing amounts of BTC (or any coin) in a mobile hot wallet or any hot wallet you're an idiot.
PHONES ARE NOT SECURE. PCs are not secure, Macs are not secure.
Treat any crypto on a phone (or any hot wallet) the same as cash in your wallet in your pocket. It can be gone at any moment. Due to theft, bad luck, or a host of other reasons.
Cold storage, yeah different world. I used to say my phone was worth more then the crypto on it. Now, I have a bit more stored on it then I should and well my phone is older and worth less, but that's on me. Not you, not coinomi or anyone else.
-Dave