Update July 2nd: After the changes were announced to go into effect (and the effects of related changes have been noticed), it appears that everything is continuing to work as previously from scriptbin's point of view.

The short answer: most probably not, with a hint of "I don't know".

The long answer

scriptbin makes, broadly speaking, two kinds of requests to the Reddit API.

The first kind is everything included in handling logging in, which means starting an authentication, getting a response back with a "token" representing someone who's logged into Reddit and then making a request using that token to see which username that account has.

The other kind is done periodically for all accounts that have logged in, to check if they still exist. If they don't, this marks them as "no longer verified to exist", which automatically deploys the "will" functionality where some things can be hidden when the account is deleted. This check is done in the background as parsimoniously as is practical; not one request per second and not even one request per five seconds.

Reddit's upcoming changes include two salient details. First, the requests are rate limited according to new rules. The rate limits at the time scriptbin was created was already 30 to 60 requests per minute depending on circumstance and to the best of my knowledge, scriptbin has never been constrained by this. The new limit is 100 requests per minute.

During a test period a month ago, I measured on average 100 successful logins per day, which is ~0.069 (nice) logins per minute. Taking all views of the login page as an attempted login (which it very likely wasn't, this includes Google indexing it, people just reading and so on), there were 450 login attempts, which is still ~0.31 login attempts per minute.

Now, more and more people do use scriptbin. Assuming the current rate of percentual growth, the number of accounts will roughly quadruple (4x) in two years. Assuming that login attempts go up by 10x, significantly more, this is still ~3 login attempts per minute.

In other words, scriptbin should be well below the number of requests per minute, even if counting each login attempt as 5 or even 10 separate requests. If there should be a paid tier to extend this quota slightly (double or triple) for non-extortionate pricing, I would have no issue footing the bill for this if necessary.

NSFW

The second change is the policy change to not allow "NSFW content". Quoting:

Reddit will limit access to mature content via our Data API as part of an ongoing effort to provide guardrails to how sexually explicit content and communities on Reddit are discovered and viewed. (Note: This change should not impact any current moderator bots or extensions.)

My reading of this is that posts inside NSFW subreddits, or NSFW-marked posts in other subreddits, will no longer be visible through the API. But scriptbin does not deal with posts, it deals with users. There is some amount of uncertainty whether "mature content" will include users who have checked the checkbox in Reddit's setting to "allow access to NSFW subreddits", but this does not make sense. Authenticating every Reddit user but suddenly not the ones who have the setting checked to see porn is not desirable behavior since "mature content" may have nothing at all to do with what you are authenticating them for. So, I am almost certain that the current functionality will remain intact.

To summarize

scriptbin is not in danger of running up against the limits any time soon. But enough has happened over the past few months and past few weeks and days in particular that I will not claim to be certain of Reddit's interpretation. There's also a significant probability that something will change about the current plan either before or shortly after it goes into effect.

And as always, Reddit has always been allowed according to its own terms to choose to stop service to any client at their discretion, supported by or independent of any other provision. One way or another, whether logging in via Reddit will continue to work is ultimately up to Reddit.