As stated, it would really help if you were more specific about what is entailed in "mind-reading". But let's compare it to some real-world scenarios.
In normal speech, or when I'm typing like right now, I can be simultaneously thinking about the concepts I'm trying to convey, the speech/text synthesis, that Star Trek episode where Data rattles off a list of mental processes he was considering while kissing his girlfriend, how I should probably be in bed but am instead on Stack Exchange, the fact that I'd really like to get in an hour or so of Fallout 4 so I should type this quickly, and a number of other things that take less precedence like how my right foot has been resting on my left leg for quite a while and the pain in my left leg is increasing but isn't yet bad enough to necessitate moving my foot.
I would expect that reading someone's mind would be similarly non-linear, so A) you're not somehow reading every single little process in their head at once (it would be impossible for you to process that much data anyways unless you completely stopped processing any data in your own brain which would be a rather fatal way to read minds) and B) even if the entire mind-reading process turned into garbled nonsense, the rest of your brain would still be wondering whether that rumbling in your stomach is from the nachos you had at lunch or the giant soda you bought on the way home even though you know you're supposed to be cutting back. Like watching a camera that's watching the screen ad infinitum doesn't somehow cause your brain to hardlock. You just say "whoa, trippy!" then go back to finishing your soda because you'll cut back tomorrow.
I'm not sure how typical this is, but I commonly experience dissociated cognitive functionality, where one aspect of my thoughts appears as another entity in my head. At its simplest, it's just a bunch of voices screaming different things (or sometimes the same thing), with the most pressing urges being perceived as the loudest voices.
In a more interesting case, I often tell myself I need to accomplish some task. At that moment, my mind splits into three pieces. There's my self, then there's the responsible guy, then the lazy guy. In a heartbeat, all three of us know exactly how the conversation is going to play out. I tell the responsible guy I know he's right, but I agree with the lazy guy (who is at that moment telling me he already knows I'm going to slack off so stop bothering to play out the conversation that I'm currently having with the responsible guy who obviously is actually just a facet of me) and remark that it's stupid that I'm having a conversation with myself when I already know the lazy guy is going to remark that I'm going to remark that I agree with the lazy guy and am in fact going to just be lazy.
And then sometimes I'm lazy, sometimes I'm responsible, and sometimes I realize it's not even the right day and I don't actually have anything I need to do. Turns out that my own mind isn't capable of figuring out what it's going to do thirty seconds into the future with very good certainty, despite the fact that there are three voices in one head in complete agreement.
(FYI, the pain in my left leg just got to the point where it necessitated moving my right foot.)
Similarly, I would expect that the act of reading someone's mind which is reading yours would create instabilities because the two minds can't perfectly predict the actions of the other. So the other mind tells you a lie about your own thoughts which you believe as the other mind realizes it made a mistake, then the paradox is perceived differently by each mind, which amplifies the discrepancy. This forces the two minds to act with agency despite seemingly having no choice at all.
(And I just realized I spent more than 20 minutes writing this and won't get an hour to play Fallout 4 and am debating whether I should just go to bed or bother playing a little and risk going to bed even later and being really tired tomorrow which will make me less likely to finish my homework when I get back from work. These thoughts occur to me as I proofread once before hitting submit in another example of non-linear processing.)