"To do this or do that" or "to do this or *to* do that"?

Solution 1:

Either is grammatically correct: eliding the to would be called ellipsis, and it is normal in English. The second to is redundant when considering the previously supplied grammatical context. Consider the following ellipsis:

Original: To change your preferences or to change your subscription list, click here.

Ellipsis: To change your preferences or your subscription list, click here.

Here, the second to change is redundant, and can grammatically be removed. You could also omit the second your:

Ellipsis: To change your preferences or subscription list, click here.

While either will (almost always) be acceptable, ellipsis is generally preferred because of efficiency.

Solution 2:

Disambiguation. Please repeat the to; after all saving two alphabets does not count for efficiency.

Let the user not be taxed with a grammatical ellipsis. (I had a mind to say 'Let not the user...'), but why not make it simpler.