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Having dealt with I&N ourselves for years (my husband is also a permanent resident), I can tell you if all of the spellings on ALL of the documentation (ie; your green card, birth certificate, SS card, drivers license) don't match, you will have to get them corrected or explain why the spellings are different.
Save yourself a lot of headaches and go ahead and get your documentation fixed. It will save you potential problems in so many ways, not just with your citizenship, but with the IRS and other agencies you may have to deal with down the road.
It may not actually hold up your citizenship, but if they catch and question it, it could set you back months on actually getting the process completed.
Please let me know if I can help further.