There's no "should" or "should not" when it comes to having feelings.

So far so good.

They're part of who we are

Indeed.

their origins are beyond our control

This gets somewhat misleading. While the origins are, the feelings themselves are not.

When we can believe that, we may find it easier to make constructive choices about what to do with those feelings.

A missing option here is to deconstruct the lightning-fast reasoning steps from the "origins" (e.g. "he downvoted me!") to feelings (e.g. "I am upset!") and see where this chain can be broken and reforged into something more desirable (e.g. ...?).

In a more engineering way of describing it, it is not only possible to close the feedback from feelings to "origins", but also to break the feedforward from origins to feelings. The feedforward part is largely intuitive and is harder to analyze, but in some cases it is much more useful.