If a student takes Algebra I his freshman year versus Geometry, and then he follows the math program that would be Algebra I, Geometry, Algebra II and then finishes with Pre-Calculus his Senior year, will that limit any choices for applying to a college versus starting with Geometry and then moving forward from there and finishing up with an AP class his senior year?
This is an excellent question and from my experience the answer is yes.
If the student is strong in math and possibly wants to major in any discipline requiring math, such as Comp Sci or Engineering or even Business, then getting to Calculus in senior year will be important.
If the student wants to apply to very, very competitive colleges, then Calculus can also be important. (An exception to this: if the student has a very strong/cool hook, but that is rare.)
So while not all students need calculus, you DO need it if you want to major in a STEM or Business field. You can take Calc when you get to college, but it will be more difficult and certainly it will move faster.
It is also often expected of top applicants applying to top schools in even humanities majors, unless that student has VERY compelling selling points elsewhere.
Hope this helps!
PS–Any student can take Geometry in the same year as either Algebra 1 or Algebra 2, since these concepts do not build upon one another in most cases. And students can always take a summer math class to get ahead. They can move ahead by a whole year, but it is challenging to do a year of math in 6 weeks in the summer.