Can it? Maybe. It’s not impossible; but it isn’t practical and most ISPs limit their shenanigans to grabbing your unencrypted DNS requests.

Will it? Probably no; aside from the previously mentioned DNS redirections; they’re not interested in most people’s packets, only in how many they deliver.

Should you care? I won’t tell you not to take precaution, but I do urge you to consider your threat model carefully and consider the tradeoffs. When Security & Privacy goes up, Convenience and Functionality WILL go down. Balance your needs. Don’t put yourself in a state of Privacy fatigue.

Are there easy fixes? Maybe. I think a VPN or using Tor would solve your concerns here anyways; it’s not required that your modem be running OSS that you can control. If you can achieve it; that’s still good for you; but it’s not something to be sweating if your modem isn’t capable and your invasive ISP is the only effective option.

There is exactly one Fritzbox (Modem+Router) that can be flashed to dd-wrt, but only if it hasnt been patched by upstream firmware

In an absolute sense, yes a modem can spy on you by hijacking requests and redirecting them to controlled locations. We use TLS to prevent this, even stronger with technologies like HSTS.

Does this happen in real life though? More then you think, but less of an impact then you think.

Some US providers will hijack DNS requests and redirect them to their own DNS servers, but this can be solved with DOH or DOT.

TLS interception is a thing but it requires the device you are using (phone, PC, tablet, laptop) to have a root certificate installed that the ISP also controls. Almost all browsers will only install root certificates from root certificate providers with good standing and have no quarm in untrusing the root certificate if things go badly.

the questions of can they spy, and will they spy are different questions. at some US ISPs (at least the one i am at) the modems usually are only monitoring performance, ie number of packets, errored and discarded packets for troubleshooting. as far as the modem which i will assume is just a layer 2 bridge to your provider, usually not a whole lot going on there due to costs of the hardware. where the privacy violations are going to occur in the access equipment or core. this is what your modem connects to, then your traffic crosses on the way to the “greater internet” if your not using a vpn to outside of your provider, there is no way around it, they can and probably do tap into what your doing. a lot of them it may not be overly nefarious, i know my company does not sell customer data, and we generally only access it for troubleshooting and bandwidth analysis for upgrades, or as ordered by a court for law enforcement.

if you use a router from your isp almost every manufacturer is trying to sell all these different analytics and dpi that basically tells us what websites customers are visiting and how much/type of traffic to those sites, but directly from the router. same, or greater level of privacy violation as that can see local traffic on your lan, as well as watching wifi connection strength and scanning to see air quality and neighbors for “troubleshooting” or to sell access points.

Block the ISP DNS and use your own on the router level.

You could look into wireguard or VPN on the router level.

Probably OpenSense.

As long ad your device has a IMEI though not like it matters.

There’s probably a million other things you would need too. Make sure your browser doesn’t use its own DNS, eg, Firefox + CloudFlare by default.

I assume you could theoretically split traffic up over multiple ISP’s making it a PITA to try to make sense of.

Also obviously separate trusted & untrusted devices, WiFi and wired into separate networks.