In Jest describe block, only one test passes at a time when using getElementsByClassName

Solution 1:

No, getElementsByClassName is non-intrusive. As in, calling it is not supposed to make any change to the DOM being queried.¹

You're not showing what renderComponent() does and it might be relevant. However, from what you describe, calling it once per test instead of once per test suite should fix the problem.²
This should work:

let container;

describe('Component', () => {
  beforeEach(() => {
    container = renderComponent().container;
  })

  it('Renders test1', () => {
    expect(container.getElementsByClassName('test1').length).toBe(1);
  });

  it('Renders test2', () => {
    expect(container.getElementsByClassName('test2').length).toBe(1);
  });
});

¹ JavaScript is fluid and powerful. One could, for example, write a getter which mutates the target, instead of just reading it. But the chances of such an anti-pattern being used inside the tools provided by a testing library are low.

² This shouldn't be seen as a "hacky way of making the tests pass". It's the proper way to test. Your tests should not be re-using the same DOM, as you don't want any changes to that DOM to propagate across multiple tests.