How can facultative anaerobes exist without catalase?
There is another class of peroxide decomposing enzymes called peroxidases. These enzymes can catalyze the reduction of $\ce{H2O2}$ to water using an electron donor. However, unlike in the catalase reaction, the electron donor is not another $\ce{H2O2}$ molecule and no molecular oxygen is produced. Thus their presence would not be detected by the typical spot catalase test (which looks for gaseous oxygen generation). For example, NADH peroxidase catalyzes the following reaction to protect cells from oxidative damage:

$$\ce{NADH + H+ + H2O2 -&gt; NAD+ + 2H2O}$$

Thus catalase negative organisms can still have a means of protection against $\ce{H2O2}$. You can read more in this textbook, specifically the section titled "Oxygen Toxicity".