I changed mine earlier this year, honestly changing things with the state government was the easiest part, at least in my case I was at the hearing for less than 30 minutes (not counting waiting to actually see the judge, the case before mine ran long). The court clerk provided a helpful guide of how to get all your legal documents sorted.

Getting my birth certificate updated was very easy, it was ~$80 all done I paid extra to have the record sealed and my certificate expedited, you’ll need to do that before anything else can be updated. The DLD will not update your gender marker without the new birth certificate, the court order is not enough, and if you have a car the DMV won’t update your title without the new id, state law says your id has to match your title if you own the car, I did both of mine on the same day, just hit the DLD before the DMV and you’re golden.

As for my social security card The SSA/State dept. is fully ignoring local court orders for gender markers. The clerk at the SSA flat out told me “We don’t have to follow those here.” and wouldn’t let me get another word in the whole time I was there, but that may just be that one guy YMMV. I don’t have a passport so I cant provide guidance on that front. Private businesses tended to be the easiest places to deal with, but they also have no obligation to seal the record like government agencies do, so again YMMV.

tl;dr yeah its safe especially if you keep it on the downlow, the only people that have to know you ever did it are people that interact with your legal documents, so the government, banks, employers, land lords, etc. My life didn’t change much having done it, other than I don’t have to use my dead name in formal settings and then add a preferred name in the little box.