1. Science as the body of knowledge
2. Science as a method / approach
I also find that mixing the meanings/perspectives/intent up in a single conversation is common, sometimes accidentally sometimes intentionally.
In my ignorance (ComSci major, so not a real science :), I would describe myself as extremely positive / confident to "Science, the approach/method" and, through that approach, pragmatic about the "Science the current body of knowledge".
In other words:
Yes, there are very much limits to what we currently know, and some of what we think we know will turn out to be wrong, subtly or catastrophically. There are definitely huge limits and uncertainties to Science the body of knowledge!
But, acknowledging it is kinda the point, and the best way to figure it out that we are currently aware of is through scientific approach. (I've just realized I might even have become a zealot that you describe, because I can't even figure out what a plausible & feasible alternative method is, if your goals are to actually figure things out. To that point, I find humility and skepticism about your current science body of knowledge a crucial part of science the method, something which most other methods lack).
I find distinction is crucial especially in political and religious discussion frameworks. Otherwise, I never know if I agree or disagree with statements regarding "limits of science" etc.
(This is all further mixed up by zillion of daily popular articles where "Science says that [...]!!!" or "[...], scientists find", which... ugh, oversimplify at best and deceive more likely)
What are your thoughts?