@tohecz: Thomas's Q is closely related to the questions I referred to, but it seems he's suffering from a problem that's not addressed in these.
I tried to use the selnolig package to selective disable the s_t ligature (\nolig{st}{s|t}) but that also stops the longst ligature from being used.
If I understand correctly, you're expecting selnolig to differentiate between an s and ſ. You're not providing an MWE, but I'm assuming that in your case selnolig just can't differentiate between the two because you don't -- I guess your text only has s and s, so there's nothing selnolig could do for you.
Educated guess: entering your ss correctly is going to produce decent results.

selnolig disabled. Minion Pro, all available ſ_ ligatures as well as c_t and (inappropriate?) s_t are present.

selnolig enabled. As above, only s_t is gone.
code:
\documentclass{scrartcl}
\usepackage{fontspec,selnolig}
\setmainfont[Ligatures=Rare]{Minion Pro}
\nolig{st}{s|t}
\begin{document}
The ſide attraction for moſt ſpectators was the mustard
\end{document}
How about the ſ_t? -- I don't have Hoefler Text, and Minion Pro doesn't have an ſ_t (technically, it does, it's just indistinguishable from unligated ſ t). But, for example, EB Garamond does, and it's not affected by \nolig{st}{s|t} (q.e.d.).
PS: if you're planning to reproduce early 19th century style, Hoefler Text (as well as Minion) will be a bad choice. It's off by at least two centuries, as is obvious from the two Encyclopædia Britannia pages (from the second one even more drastically so than the first). Have a look at a Hoefler's Didot instead, maybe Old Standard or -- inexpensive and most appropriate -- Miller from Font Bureau.
update
Looking at your own answer and your insisting on the idea that a mere Contextuals=Inner is going to suffice to produce correct results -- what needs to be stressed is that correct ſ usage is not as simple as »replace all non-final s by ſ«. I suggest you have a look at how the ſ was handled in the period/the culture whose style you're trying to reproduce. In what contexts was it used? When was a s used instead? Think compound-word word boundaries. What ſ_ ligatures were available? Think, among others, ſ_s. In what contexts were which ſ_ ligatures appropriate/inappropriate? Again, think compound-word word boundaries. What was considered a compound word in the first place? etc.


Further reading: http://babelstone.blogspot.ca/2006/06/rules-for-long-s.html
lualatexis currently the only option available. Either way, that question asks basically for the same thing as yours. Tell us whether they are significantly different. If not, they can be marked as duplicate. – yo' Jun 01 '13 at 08:51Contextuals=Inner(to generate long-s characters automatically in initial and medial positions) currently works with XeLaTeX but not with LuaLaTeX. If you want to enable the just thectligature but no other "rare" ligature, you can do so in LuaLaTeX using an OpenType feature file, but you'll use the automated use of long-s glyphs. For now, theselnoligpackage only does ligature suppression; selective enabling* of ligatures isn't (yet) one of its capabilities. :-( – Mico Jun 01 '13 at 21:01Innerfeature is not an appropriate option for taking care of corrects/ſplacement. The underlying mechanism is indifferent to the complex conventions that governſusage in a given cultural/historical context, and it's indifferent to the semantic issues that are involved as well. UsingInner, your output will be full ofsucceſſfully miſdirected Doomſday tranſformers from Peterſburg. There's no alternative to entering theſs correctly in the first place -- which by the way is exactly what we have Unicode (and Xe/LuaTeX) for, right?:)– Nils L Jun 02 '13 at 08:29sand I depend on the XeLaTeX optionContextuals=Inner. I also only havesandsin my text and do not differentiate betweensandſsoselnoligis of no help --selnoligis yet to support the feature to selectively enable theſ_tligature. – Thomas Tan Jun 02 '13 at 19:17swithſand then selectively enabling the ligaturec_t. – Thomas Tan Jun 02 '13 at 19:24