Pretty much as per the subject line - can joining House Telvanni be avoided?

Yes. Just don't work for Neloth.

It wasn't really joining as Neloth only says you are in and says he has a chest and bed for you. She says on our return to Morrowind we will be treated as royalty, in a decade or so.

On a matter of principle if you do not want to join then you should not go down his quest line as he did not offer me an option of not joining.

Well it has no real perks besides a bed in Tel Mythrin.
Why the need to avoid it?

Well, roleplay reasons - that you can only ever join one Great House. I'd rather my chars joined Redoran than Telvanni.

Well as far as I know, Redoran membership isn't extended though you could take getting Severin Manor as your admittance. Make some Bonemould Guard Armor. Something like that.

This.

You can buy and sell stuff from Neloth and his apprentice, but as long as you don't do his quests, he won't ever make you a member of the House.

why the hell would you want to do that?

House Telvanni are the mad scientists of Morrowind and of the Elder Scrolls series, can't understand why you wouldn't want to work for the most hilarious and badass wizard in all of Nirn?

I joined his grp because if there is ever a DLC where there is massive war against the Thalamor I hope that by helping Neloth out as his guinee pig test subject and occasional fetch errand runner Neloth might in return join the battle and get to see him go all out Rambo with my team to push back the Thalamor forces (hopefully)

I enjoyed Neloths remarks everytime I questioned his requests. Whoever wrote his txt reply lines should be treated to lunch.

For Roleplaying purposes you can considering it the ramblings of an isolated old man. He clearly isn't in contact with his house as he says it doesn't mean anything that you are in the house until you both return to Morrowind's mainland.

You could also consider it as a lie that you tell him in order to get his assistance.

Well, seeing as there is no love lost between the Dunmer and the Aldmeri Dominion... the Dunmer could possibly be convinced to lend their aid in any anti-Thalmor attack /battle plan.

Yes defeat the Thalmor and feed them to the Falmer!

even if you finish neloths quests, you arent really a member
same as the redoran- you are a citizen of ravenrock and have their thanks, but they never say you are a house member i dont think
and even though neloth says youre a member in the end... come on, its the telvanni
half the time they dont even bother to see whos a member or not
your pretty much just a decorated merc for neloth by the end of his quests, despite the title he gives out
in my opinion the only actual telvanni members are the high wizards like neloth
all the rest are pretty much just there to do chores and experiment on

Basically what everyone else has said.
You technically ARE a member of House Telvanni, but the only time you ever get recognised as a member is when you ask Neloth "what does it mean to be a member of House Telvanni?"
And even then, he basically says; "Bugger all untill you go to Morrowind with me."

So yeah, you don't get treated any differently by anyone what so ever. You can do the quests for Neloth to reap the benefits, and then just forget everything he said. Your RP'ing experience won't change one bit.

Yeah, hence why he turned my eyes into tentacles, after telling me to go gather stuff for him. The title doesn't really count for anything given the stuff he does to you.