First, I submit this principle "TIMTOWTDI" : [slang.org]
I routinely have multiple browsers open concurrently -- Brave, Firefox, Opera, TOR -- each with multiple extensions.
Is is rare when one-or-the-other doesn't 'get the job done'.
. . . of course, YMMV
Do you mean access or blocked by an wrapper? Most of the time, my biggest problem is are those wrappers asking you turn off your ad blocker, which I don't have. I do however make use of Firefox's tracking blocking and the Privacy Badger addon. I've also discovered that most of those wrappers can be circumvented by disabling javascript (another addon) for the site.
I almost forgot another strategy that one might have to use in conjunction with disabling javascript: deleting site data and cookies for that particular site.
Blocked by ad blocker, subscription, or javascript turned off . . .
@bingst I delete site data/cookies regularly, use private windows, and at times give totally bogus info.