Update: Answers extracted from comments.
Thanks a lot to everybody who answered in comments.
leo[l_] := Reap[Sow[#, #] & /@ l, 1 | 8, #2 &][[2]]; jm[l_] := Function[p, Select[l, # == p &]] /@ {8, 1}; kgl[l_] := Select[l, Function[x, x == #]] & /@ {8, 1}; mar[l_] := With[{p = #}, Select[l, # == p &]] & /@ {8, 1};
Out of curiosity I decided to run simple benchmark to check performance
Benchmark[f_, n_] := Module[{l, results, samples}, RandomSeed[314]; samples = Table[RandomInteger[{1, 100}, n], {10}]; results = Table[First@AbsoluteTiming[f[l]], {l, samples}]; Mean[results]]; testRange = 10^# &@{3, 4, 5, 6}; TableForm[ Table[Benchmark[fun, n]/n, {fun, {leo, jm, kgl, mar}}, {n, testRange}], TableHeadings -> {{"leo", "jm", "kgl", "mar"}, testRange}]

The results are normalized over list length. Interestingly kgl[] is about two times slower than jm[].
IMHO the Select[l, Function[x, x == #]] & /@ {8, 1} (by @kglr) is the most visually appealing.
It was also asked why do I care if all I need is just making two simple Selects?
I think it's more clear and concise to have one line that does something twice rather than having two almost identical lines. My original example is oversimplified probably.
Imagine I want to select all prime numbers and also all numbers that are prime squared. If I use syntax by @kglr I can do
{primes, primeSq} = Select[l, Function[x, #[x]]] & /@ {PrimeQ, PrimeQ@Sqrt[#] &}
Which is very self explanatory.