Here’s my take on this.
I can see why you’d want to avoid untrustworthy sites. For public profiles, the most straightforward method is using a web browser in incognito mode. You can see a few posts before Instagram usually blocks you with a login wall, and you can’t view Stories. It’s anonymous, but the view is very limited.
Another option is creating a secondary, anonymous account. This gives you much better access to public profiles and lets you request to follow private ones. However, it’s not technically “without an account,” and your follow request might be ignored.
Dedicated monitoring tools are a different category entirely. They typically provide much deeper access by working from the device itself, bypassing the public login restrictions. It really comes down to a trade-off between simplicity and the level of visibility you’re looking for.