Doctors do. A few factors need to be kept in mind especially for heart patients who have had a PCI Stent or acute MI in the past 6 months, stroke or DVTs history. Also women above 45 who are going through menopause on Hormone replacement therapy and couples on Oral contraceptives all have an elevated risk compared to the normal population.
I'm sure no trained physician will be an anti-vaxxer because they are literally trained in every aspect of it from its history, merits and consequences when things go wrong. So please if any of your parents or yourself are on long term medications or are known cases of chronic illnesses, besides the usual like diabetes or uncomplicated hypertension, having a word with your physician is a very good idea. Nothing to lose, potentially a lot to gain.