There are two different debates in the foundations of mathematics that are confused here.
The first debate is whether the continuous line is made up of infinitely small points. This was settled by the development of the real number system which allowed each point on the line to be expressed algebraically by a decimal expansion.
The second question is whether the real numbers were enough or whether the line had additional points on it so that the corresponding number system failed to satisfy the Archimedan axiom (in other words, points greater than 0 but less than ALL the numbers 1, 1/2, 1/3, 1/4 , 1/5, ... ).
The second view was used by many mathematicians in the 17th through 19th centuries to develop calculus in a way that was NOT logically rigorous, and which was CORRECTLY criticized as incoherent by Bishop Berkeley and others, culminating in the logically rigorous and irreproachable treatment of Cauchy in the 1830's, further developed and modernized by Weierstrass and Dedekind a generation later, which used limits to avoid infinitesimals and allowed completely convincing proofs to be given.
It was not until Abraham Robinson in the 1950's demonstrated that infinitesimals could be consistent if one was much more careful than the 17th-19th century mathematicians had been, that alternatives to the standard real number system were taken seriously again.
Points infinitely small? Always ok. Numbers as intervals between points infinitely small? Properly rejected as non-rigorous and unnecessary prior to 1960; now accepted as capable of being made rigorous but still not necessary.
Modern physics casts doubt on the scientific necessity of the earlier view of infinitely small points on the line represented by the standard real numbers, because of the existence of a tiny fundamental length scale, so the argument is not settled by an appeal to physical reality.
The version of the real numbers we use, given by decimal expansions or rational approximations with no infinitesimals, really is logically better, as was first recognized by Archimedes two millennia before Calculus (which he invented) was rediscovered by Newton and Leibniz. Archimedes used infinitesimals as a mental shortcut to find results that he later made rigorous by using perfectly valid limit arguments of the kind Cauchy later generalized.
Confusing these two issues in order to contrast modern irreligious freethinkers with dogmatic old Christian fuddy-duddies and bask in political self-satisfaction is tendentious and fundamentally wrong.