It's unpatriotic to want to abolish the monarchy
That depends how you define patriotism. If you think it's about putting the interests of one family above those of ordinary Britons, then yes it is.
If, however, you think patriotism is wanting the best for your country, trusting your fellow citizens and putting power in the hands of the people, then you can't get more patriotic than republicanism.
Britain is a fantastic country, full of amazing people. We know that one of them could do the job of head of state at least as well, and probably better, than whichever member of the Windsor family is chosen for us.