It can be! How old are you? Have you had shoulder surgery?
Please consider advice from your Physical Therapist on this matter.
General guideline that I use as a practicing PT for 39 years is that if you are > 45 yr old and have had any shoulder symptoms then don’t do down dog. It places you at too large of risk. Find other more friendly shoulder exercises i.e. wall push ups, tricep extensions or dumb bell chest press.
Is Yoga Too Hard on My Shoulders?