Should I let my kids try to skip their current math class to move on to Algebra 1 in 7th grade?

For students who are capable, I agree.

On that I disagree. No reason, IMO, to retake basic calc 1 and 2 in college, particularly if the college gives credit for AP/IB or offers a challenge exam or as @ucbalumnus states, the college/major requires proof-based calculus.