Circular saw blade clogs nonuniformly

Back in the day when I used to put up vinyl siding, I found that the best way to cut it with a circular saw was with a cheap 140 tooth plywood blade installed backwards (to give the teeth a negative rake and prevent chipping):

For really hard plastics, I've used a diamond abrasive blade before and that did a great job (these are incredibly expensive if we're talking about a single cut though). I would imagine an abrasive blade for cutting metal would do just as well though:

You should be able to pick up either of these for less than $5.

Wear good safety glasses and do a trial cut first with whatever option you go with - plastic will chip long before it will bind the blade in most cases, and these can be both sharp and high velocity.

Despite what you might believe, those adjustment levers on most tools are not calibrated very well. Even on my table saw I regularly use a simple plastic 90-degree triangle to ensure my blade is aligned to the table. This is part of owning any tool and it's worth a few moments to verify everything is set up properly. A more expensive tool will simply buy you more time between calibrations but all tools should be checked with regular use.