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

Yes depending on the situation and people involved ....

When my father-in-law started in on me from the first moment, I exercised the respect I was trained that he was due, and smiled. He was a WWII Minesweeper Officer. When his youngest son, a non-service member started in I gritted my teeth for a time until I finally decided ENOUGH. Took him aside and told him hadn't earned the right to rag my ass. Shut him up, and because he couldn't understand why it was OK for his dad but not him, he hasn't had a lot to say to me since. Broke my heart.

No I don't care what we are called.It doesn't bother me as long as I know my MOS and that I am a Marine.

It like any other thing is a word it depends on how you use the term and if they have the same leeway to say the same thing back as in squid. Bot bothered by it but marines are devil dogs they earned that.

Marines do not care (always a few exceptions). throw a derogatory name at them and most will embrace it, that's how all the current nicknames originated; Jarhead, Gyrene, Leather, Leatherneck, Tuffelhunden, Devil Dog, Pogue, Grunt, Knuckle Dragger, etc...

My family has a long tradition of military service. Both of my grandfathers served in the US Army and Royal Army. My Dad, brother and myself all served in the Air Force. I've been called Airedale, Wing Wiper and other derogatory terms. But, if it comes from another military member, no matter what service, I took it in the spirit intended. Civilians make it an insult. Inter service rivalry will always be part and parcel of military service. So to my brother's in arms...Grunts, Jarheads, and Squids, you have my undying respect. But I will still throw out the friendly insult now and again.

God Bless You all!

Only if the two of you don't like each other, but the Marine has more shit talking rights due to branch

As a former Army guy, that has 2 sons that served Army, 1 son that served Marines, another son that is getting ready to leave for the Navy, a son-in-law that was a Marine, and a brother that was Air Force, it gets pretty interesting around our family. We all kid each other equally, call each other endearing names and joke. But we stick together as having all served. I am proud of my Grunt sons, Jarhead sons, my squid son, my chair-force brother and anyone that served.
I think anyone that hasn't served, has to be taken in context. Some are well meaning and don't deserve to be beat down for using monikers to identify us, but sometimes, the person might not be well meaning. That's when we should just walk away, because they just won't understand and don't deserve our time. Keep your chins high, know you are among a special brotherhood, and be proud.

I served proudly, you can call me jarhead, leatherneck, or asshole...I was and always will be a proud Marine!

I've always seen it as a term of endearment. However if you've never served and speak the words like Jar Head, ground pounder, puddle jumper, fly boy or squid I will absolutely get offended.
If these offend an active duty service member i'd assume they've never had sand I their boots or salt in their eyes.