If you're doing really complicated stuff then you at least need to understand algebraic logic and concepts. You'll also need to understand stuff like logarithmic scales for optimization. But it's entirely possible to go years without using any math, especially as a website developer. I'm about as senior as you can get in the field, and I've only had one job for around 4 years where I used advanced mathematics on a regular basis. That's 4 years out of a 25 year long career.

That said, a CS degree is going to require all of the math classes as part of the curriculum. My degree program involved fun classes such as finite mathematics, statistics, trig, etc.. If you're doing a program that requires advanced mathematics courses, for goodness sake do them all in a row!

TLDR: it depends entirely on the job. Jobs that are data intensive, with data manipulation, hardware interfacing, and automation type jobs will require more math than jobs like making cool-ass interactive websites.

Edit: PS, I suck at math. I've always sucked at math. Yet I'm what most people consider an amazing engineer. Weeee!