The Supreme Court has become largely politicized over the last few decades. When you strip away all the noise, the reason why some people are protesting this nomination boils down to the fact that their side (Democrats) did not get to appoint the next judge and this particular judge's political views do not align with theirs.
Of course, they will not flat out admit this, so a set of cover-up reasons are created instead, mainly:
Republicans' hypocrisy: During Obama's last year in office, Republicans argued that no president should get to put a judge in the Supreme Court during an election year, and used this to justify their blocking of Obama's nominations. Of course, they didn't have to come up with any justifications; they had complete authority to block Obama's nominations due to the simple fact that they controlled the Senate. Now, Republicans have reverted their argument, and have decided to nominate this judge on an election year. Again, they have the authority to do this due to the fact that they still control the senate, but their actions does show a level of hypocrisy.
In the end, it all comes down to politics. Some people don't like this judge's politics and the president nominating her, but "I don't like them" does not make for a good argument, so instead they point out to Republicans' hypocrisy from the past to protest the nomination. That doesn't make for a good legal argument either, since everything Republicans have done they are legally allowed to do, but to some it might make for a good moral argument at least.