I have been in this situation myself: a company that wanted to hire me presented me with a non-compete agreement. I naively think that I should expect contracts and obligations that I sign to actually be upheld by all involved parties, including myself. If I signed it, nobody would fire me from another position — because I don't violate contracts that I sign, and I wouldn't apply for another position in the same field.
Instead, I declined to sign it in the current form, explained my problems with it to an HR, and one day later got an edited agreement that had a non-compete with a reduced scope (only companies making similar products).