Can only speak to CNR, not Engineering…My daughter is a rising sophomore in CNR and did not take calculus in high schools (for similar reasons: she had gone to an arts-focused charter school for middle school which was not strong in math, then entered a different high school and was placed in Math 1 in 9th, then Math 2 in 10th, Math 3 in 11th, then AP Stats in 12th. Her high school doesn’t allow doubling up in any subject, so once you’re on the “regular” track for math, there’s really no opportunity to get off and reach calc by 12th).
So for CNR at least, you can still be competitive without calc.