Will rejecting more papers than I accept reflect negatively on me as a reviewer?
It is of course impossible to say if you are overly critical. But, some statistics might help. With prestigious journals the rejection rate might be 90% (very high in any case). I am Editor in Chief of a smaller journal and we have a steady 50% rejection rate. The extremely high rejection rates in some journals come from limited space, in my case we simply impose strict guidelines and the rejections come from reviewers assigned by associate editors. So the rate in our case is fairly certainly upheld by what the community sees as acceptable or not.

So if you end up finding you reject large numbers (at least around 50%) I would not say that it is out of the ordinary. I do not of course know what typical rejection rates are in the journals for which you do reviews, so the number may of course vary.

So getting to the question of how this affects you. I very much doubt that you get a negative effect by being a fair reviewer. If you do many reviewes over time and you are not considered fair, I am sure you would notice the numbers of appointments dropping. If you get re-invited by the same journals/editors, I think they appreciate your work and I would take that as a sign that you do fine.

Should you try to adapt to the journal? In general, no. You should apply your knowledge and understanding to provide a critical review of the submitted work. An editor should take your comments along with comments from one or more additional reviewers and provide a recommendation to the authors. You are not solely responsible in this process! If the journal is such that it publishes material with which you are familiar but where its audience is in a  different field, you may consider handling the paper differently, but obviously not ignoring errors and misconceptions.