It's not a very felicitous sentence, no matter how you slice it, but if you can only change one part (or neither) then your best option would be
I will never marry anyone, but will be a dancer.
This structure does have the same tense in both clauses, simple future with "will". The verb in the first part is marry and the verb in the second part is be, so in the corrected sentence we have will [never] marry and will be.
This is a little confusing, because often the verb be is a helping verb, but here it is actually the main verb of the second clause. In the original sentence the two clauses didn't match, even though both had "be", because the first "be" was acting as a helping verb, so marry was in the future progressive tense: will be marrying.
The corrected sentence means something like
I do not plan to ever get married; instead, I will be a dancer.
The sentence is setting up "being a dancer" as an alternative to "marrying anyone", so only one or the other can happen, not both. Note that with this construction we can leave out the repeated subject in the second clause; this is called ellipsis. Some similar examples of the "I will not/never . . . but will" structure:
I will never give my assent to any address of any kind to the throne, but will now, and upon all future occasions of the like kind, divide the House (Debate in the Lords on the King's Message Regarding the Spanish Manifesto, 1779)
I will never be ashamed of my religion, but will always avow it when and where it shall seem proper so to do. (The Church of England Magazine, 1855)
I will not pursue this solution here but will simply suppose that we could adopt it if necessary. (Kant’s Transcendental Deduction, 1992)
This is a very formal and somewhat old-fashioned structure, as you can probably tell from the examples, so you probably won't run across it in casual conversation very often.