Do you consider the term jarhead and other names for the different branches of service offensive?

No as already mentioned all in the military family. Marines and sailors were always using slang names in reference to each other. Much slang of other services started in Parris Island with more cussing and vulgariety than previously thought possible. Aboard ship the sea, air, land types were questioned, how long can you balance a ball on your chin anyway ? Then there were the seal sounds and clapping hands. Deck ape, squid, paint chipper, anchor clanker, pixie cup referred to the head gear. Navy gave it right back to the grunts on their vessel with a colorful cussing. Lining up for ship chow the ice cream machine would break.
Recent events made BAM a bad reference. Fifty plus years ago it was used not in a derogatory manner. Just a nickname term of endearment for the WM.
The U.S. Air Force always treated a Marine well. They did not care for Marines off the flight line with weapons. In a uniform with no chevrons got me into a U.S. Air Force Officers Club Hickam Transport across the the base provided by a U.S. Air Force Police butter bar lieutenant. Air dale, wing wipper and odd references to being civilians were still used. No better chow or base services than U.S. Air Force.
Doggie, dog face, ice cream soldier, ricky ranger and SF were not spared. U.S. Army chow better than Marine.
Coast Guard then under the Deparment of Transportation. Duck ass navy, knee deep navy and those guys lived on a yatch. All in the family.

I try not to use the term Jarhead to describe a Marine. I believe crayon eater to be more accurate.

No, why?

Interservice rivalries are, in my opinion, an important part of the camaraderie of the branches. 99% of Marines won't care if you call the jarhead as long as you're not clearly trying to be a jerk. Just don't call the 'Sarge' Marines really don't like that.

call me anything but late for dinner... I was Army, so admittedly I'm a little fond of the term "knucklehead"

What does it matter if it comes off as offensive? That's why it's called rivalry. If you get a little stressed because some jarhead calls you a name...how are you gonna react to combat?

I like to remind them that submarines are a myth. After all, there is nothing lower than a Marine! ba dum bum, tish! But I'd never accept that from a civilian!

Jarhead is a derogatory term. It's the same as a white person calling a black person a n****r. However, if you are what you call someone else, then it's meaning isn't quite the same.

While I served on the MarDet on the U.S.S. Midway... I had a squid friend of mine once tell me the word Marine is an acronym.... Standing for Muscles Are Required Intelligence Not Expected... I was laughing so hard, I could not beat his ass for it. Now, I have a good friend who is (get this) Retired Coast Guard, he and I bust each others balls constantly. And I agree, we are all family. We have the right to bust each others chops...

It never bothered me or my dad.

Depends on the tone of voice, and the expression on the commenters face...
At 70++++ years of age I've pretty much ceased to give a rats ass myself..

I have noticed that some of the youngsters do not like the "jarhead" monicker. Not sure why or what is behind it. I think it is hilarious that some Marines still think calling an Army Infantryman a Dog is an insult. I think that went out as a insult like four or five decades ago.....ha-ha.

Inter service rivals are great for morale I'd stick up for any branch if a civilian tried to clown on them in a heart beat.
I get ragged on from former marine and seamen(lol) all the time and I rag them right back . But it's all done in good fun and respect.
It's part of the brotherhood/sisterhood of military fraternity

Nobody mentioned the term "Chairforce." Im like the majority here, if you're a civie and have never served then you have no place to make fun of the services. Other than that it doesn't bother me at all.

tradition and jocularity especially no problem coming from a service member. Could be insulting coming from a civilian with no ties to the military.

It's a friendly jab between armed forces, as long as when the bs hits the fan they have my back

I do not think it is offensive. My husband is a former Marine and is very proud of his service as am I. Sadly our pc culture has everyone being offended of one thing or another. I am Irish and I can't even make fun of myslef anymore.

Jarhead (Marines), squid (Navy), lazy (Army) that covers all the branches that matter.

Nope, not at all. If it offends, then step aside and get your big boy pants on.

Between service members it's OK. But if some Jody in the 1st cover div tries instant knife hands and a Gen Mathias throat punch