Do you usually stumble across illegal material when you browse the Internet? I don't see why it would be any different using Tor... you can still access clearweb sites via the Tor Browser.
Not only that, you can access onion sites using an ordinary browser via sites like tor2web. Using the Tor browser doesn't expose you to anything you otherwise weren't, it just makes you more anonymous.
One of the premises of the tor onion routing is traffic is routed thru intermediates.
I suppose this question is about validating if being part of the onion router is controllable and secondary (an assumption) being part of the tor mesh means you are carrying traffic that is illegal or morally questionable
Tor browser won't make you a relay.
Indeed, Tor browser comes with its own dedicated tor instance. And I don't think that it can run as a relay. Maybe with some tweaking. Also, it's only running when the browser is.
This isn't BitTorrent, you don't become a part of the network by simply using it. You have to explicitly choose to become a relay.