Naxos to Santorini for the day in early July

I would say no, its not worth it. Santorini is very hot and very crowded, especially in July. When I say crowded, when we were in Oia in July, walking through town in the crowd was like walking out of a stadium after a big game. What I would call bumper to bumper people. This can be avoided if you walk around starting at 8am, which you wont be able to do if you come as a day trip. Also, you will be there at the same time that the cruise ship crowds are there. In short, if you really want to see Santorini, even staying one night would be better than a day trip (because then you'd have the night and early morning when the cruise ship ppl leave).

Take into account the time it would take to get to the ferry port from your hotel as well as the time returning to Santorini's port for the return to Naxos, and you'll have even less time to see Santorini. If you can't manage an overnight it's definitely not worth it.

Consider a day trip from Naxos to Santorini, even if it was theoretically possible from a timing point of view,
is the worst thing you can plan on your vacation.
You will be crammed with hundreds of people on a ferry and will only have at most an hour or two to stay in Santorini (or rather in this kind of commercial center on a sales day that Santorini has become in summer)

Save your time, money, energy, and your health to keep visiting Naxos.
I'm sure that day you won't even have seen 80% of Naxos

I have recommended that day trip only for people who are in Greece either in May or September ... not in High Heat High Season! The other strategy I"ve recommended (and used, with newcomer pals) can work, IF accommodations are not already Set In Stone. (alas many newcomers book nonrefundables before figuring out itinerary completely) and IF u can get a domestic flight. Here it is:

Book your international flight to arrive at ATH airport in AM. Don't leave airport; take domestic flight to Santorini early PM same day. Enjoy sunset/dinner w view 1st night; Stay on/near the rimside view in convenient/quiet area (I like Firostephani). On Day 2, get up early AM and bus/taxi to OIA by 8:30 am to see & enjoy before cruise/tour mobs arrive about 10-10:30 am. In afternoon take Blue Star ferry @3:15 to Naxos. JOb done.

What Janet said above is the only way I’d consider seeing Santorini. I’m in Rhodes now, and the old city is a gem when it’s not thronged with thousands of zombies from the cruise ships. I was spoiled last fall having two nights in Dubrovnik without any cruise ship passengers whatsoever. Covid put the freeze on them. The hotel owner we were staying at offered his opinion; the mass tourism brought in by cruise ships ruined the Dubrovnik experience.

I understand what he meant and Santorini is another destination altered by the impact of mass tourism that puts unmanageable numbers of people in places that simply cannot handle that many people in 8 hours.
You might consider Paros for a day trip- it’s only 30 minutes away from Naxos by ferry.

Lots to do in Naxos as it's the largest of the Cyclades Islands to keep you busy without the stress, cost and hordes of tourists on Santorini.

There are several nearby islands that can offer day trips which you can look into like to Koufonisia.

Or just book a guided tour of Naxos with several types of tours.

We just returned from Greece, and I agree with everyone's advice not to attempt Santorini as a daytrip. How many nights are you in Naxos? There is so much to see and do there. We were there for 4 nights and were never bored. And didn't spend any time at the beach because the day I allocated for the beach was not beach weather. I assume you will want beach time in July, so if it were me, I would stay put in Naxos.

thanks really appreciate the advice. Has simplified the decision and reassured me that there are lots of other wonderful options.

We did a daytrip/cruise to Delos and Mykonos from Naxos back in 2009 and we really enjoyed that! We didn't really have a lot of interest in staying in Mykonos but it was nice to check it out for a couple of hours. Something like that might be a good option for you?