grammaticality - Should the verb phrases following "either" and "or" in an "either/or" sentence have the same structure?

Edwin Ashworth's comment explains the structural problem that exists in the first option: The point at which either appears creates a node from which (usually) two parallel ideas emerge. Structurally, the words preceding either in the sentence or clause apply equally to both parallel ideas. Thus the sentence

The coordinates of the points are either given or can be easily calculated.

contains two parallel ideas that logically consist of these words:

The coordinates of the points are given.

and

The coordinates of the points are can be easily calculated.

Obviously, the are in the second parallel construction shouldn't be there, and it's easy enough to get rid of. In fact, you have multiple options for avoiding the structural anomaly. For instance:

The coordinates of the points either are given or can be easily calculated.

Either the coordinates of the points are given or they can be easily calculated.

The coordinates of the points are given or can be easily calculated.

Alternatively, you can avoid the problem by dispensing with the either/or construction altogether. For example:

If the coordinates of the points are not given, they can be easily calculated.

If the coordinates of the points are missing, you can easily calculate them.

I should emphasize that I'm talking about the structural logic of your original sentence—not about its comprehensibility to people who are fluent in English and therefore able to look beyond the actual structure of the sentence to glean its intended meaning. In general, you're better off avoiding flaws in parallel structure than leaving to each of your readers the task of silently (and perhaps subconsciously) correcting them for you.