For the current savage-raid its obviously a no-go to go in alone when you're part of a static - for the simple reason of chests (you'll get less if people have already cleared it for the week). But thats the only context in which I consider such a behaviour okay.

For other content its a bit more difficult to say - in general I'd say everyone has the right to progress in their own time. Personally I like clearing content with my friends for the first time, so I'll often wait for them, but given you follow a few "ground rules" it should be perfectly fine to go ahead and clear it on your own.
For me those ground rules are:
1) Communicate with your group - specially when new content comes out, talk about wether or not you want to do it together (if you want to, pick a date!) or if its "free for all". Stick to that agreement - with new content I'm willing to wait a week for everyone (on average, depends how intrested I'm in it). If it doesnt happen til then, I'll go on my own. Again: Thats something I communicate to my group.
2) In case your raid-group still wants to run the content blind, keep your mouth shut if you've already cleared it and dont spoil that fun for them!

I used to be in an FC where the FC-leader would get outright hostile when I went ahead and cleared EX-primals and the like with other friends - and that after I had waited for him to set aside 2 hours for that content for weeks. He wasnt short on time, basically on 24/7, but always found a reason not to do that content when I asked. It was a pretty bad situation - I hated raiding because I always had to kinda do it behind his back, even though he wasnt really intrested in that content he had issues with me clearing Ex-Primals and Coils. I can only strongly advice you: Run when you meet a person like that! Its a goddamn game, you're playing to have freaking fun - not to be shamed for playing content that helps you achieve excatly that! No one has the right to scold you for that. Period.

However, refering back to my ground rules and my new FC: We're following the first rule, basically. We talk about how we want to play the content - and its okay if someone says "Hey, I want to go ahead and clear that asap!" even if the rest is like "Yeah, we wont have time til the weekend and we'll go in as group then". The important thing is to communicate about those things, come to an agreement and stick to that.
"Betraying" such a "promise" (as in: "We'll all do Savage together on friday") is not okay in my book - but not sticking to an agreement with friends would never be okay, regardless of ingame or outside of it. That being said: if the agreement was "We'll do that friday" and people dont show up on friday and you re-schedulde and people dont show up or its gets postponed again, I'd consider it perfectly fine to say "Okay, I've waited now for a while, but this doesnt seem to work right now. I really want to see this content though, so I'll go ahead on my own - everyone is welcome to join ofc, but if you rather wait for Jimmy, thats fine too!"

In general: You're playing this game to have fun - so make sure you surrond yourself with people who share your idea of "fun"! Stick to your word - but also stand your ground, when there is no word to stick to!

Please, please dont repeat my mistake and stick with someone who makes you feel miserable for clearing content a month after release without them because they cant get their shit together - it ruins your fun in- and outside of the game... and you're not paying 13€ a month for that.