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Well yes, but they also knew stars collapsed, and that something had to happen in that case. Maybe at first they thought fine, everything becomes a white dwarf or a neutron star.

But then after Oppenheimer did the math in 1930 and showed that collapse into a black hole was within the theory of relativity would you still taken the same position?

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If the theory of relativity was a person, it would not be old enough to drive or vote in 1930. :) It was an accepted theory, but it was not the wildly successful theory it is today.

Showing that a black hole was possible within the theory could just be a problem with the theory itself. Not necessarily an indication that they must exist.

This. Physics is a field of science, unlike math. They're dealing with models that keep on changing. Newton's model of F=ma is generally close enough for most things, but breaks near the speed of light. Following the model solely would give you the false idea that speed of light is just yet another number.

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