I have my macbook connected to an external monitor with HDMI and the text is blurry. A lot of peope have that problem going back to 2012.
Have you tried a different external monitor? A few years back (in 2012) I connected my Mac Mini via HDMI to a newly purchased HD monitor, and had bad results. I returned the monitor (which was made in the U.S.A. - probably the only one made here), and bought a Samsung HD monitor. The Samsung monitor works great. Your problem is probably with the choice of HD monitor; they're not all alike. Some do HDMI poorly. Samsung does HDMI well. Try switching to a Samsung monitor (and mine is paired with a Samsung sound bar) for a great HD experience with Macs.