basically my entire friend group and family is autistic so advice may not apply to NTs

i always try asking the person what they want/need from me- like if they come to talk to me and are clearly upset, i ask "hey, what's the best way to support you rn? you wanna rant to me, problem solve, share experiences?" that kinda thing. obvs sometimes people don't know what they need and may need a minute to figure it out, but it's become automatic to us now so i don't often need to ask

also just to clarify- people haven't said you're being rude to your face/made any implications you've picked up on? i've seen people talk about it too so completely understand the worry over it. also culture impacts this kinda thing a lot (as a non-american, i've personally only seen americans say its rude, but social media focuses on them so much idk anymore). if nothing else, you could preface any story with "i experiences a similar thing so totally get where you're coming from" as it might drive the "i'm not trying to make this about me, just supporting your emotions" point home more.

regardless, communication is important and the people worth sticking around should want to talk about these kinda things with you so everyone is supporting each other correctly