The best method I am aware of to handle this kind of problem is to filter by context.⁽¹⁾

SetAttributes[user, HoldFirst]
user[s_Symbol] := Context@Unevaluated@s =!= "System`";

a[x, y]/(b[x, y] c[x, y]) /. f_?user[x1_, y1_] :> f[2 x1, 3 y1]

a[2 x, 3 y]/(b[2 x, 3 y] c[2 x, 3 y])

One could include other contexts in the exclusion besides System, or use the inverse and test only for user symbols existing in the "Global`" context. Without additional examples my example is as specific as I can make it.

Regarding the unusual evaluation of the ? operator (PatternTest) please see:

• Why doesn't PatternTest work with Composition?

The best method I am aware of to handle this kind of problem is to filter by context.⁽¹⁾

SetAttributes[user, HoldFirst]
user[s_Symbol] := Context@Unevaluated@s =!= "System`";

a[x, y]/(b[x, y] c[x, y]) /. f_?user[x1_, y1_] :> f[2 x1, 3 y1]

a[2 x, 3 y]/(b[2 x, 3 y] c[2 x, 3 y])

One could include other contexts in the exclusion besides System, or use the inverse and test only for user symbols existing in the "Global`" context. Without additional examples my example is as specific as I can make it.

Regarding the unusual evaluation of the ? operator (PatternTest) please see:

• Why doesn't PatternTest work with Composition?

The best method I am aware of to handle this kind of problem is to filter by context.⁽¹⁾

SetAttributes[user, HoldFirst]
user[s_Symbol] := Context@Unevaluated@s =!= "System`";

a[x, y]/(b[x, y] c[x, y]) /. f_?user[x1_, y1_] :> f[2 x1, 3 y1]

a[2 x, 3 y]/(b[2 x, 3 y] c[2 x, 3 y])

One could include other contexts in the exclusion besides System, or use the inverse and test only for user symbols existing in the "Global`" context. Without additional examples my example is as specific as I can make it.

The best method I am aware of to handle this kind of problem is to filter by context.⁽¹⁾

SetAttributes[user, HoldFirst]
user[s_Symbol] := Context@Unevaluated@s =!= "System`";

a[x, y]/(b[x, y] c[x, y]) /. f_?user[x1_, y1_] :> f[2 x1, 3 y1]

a[2 x, 3 y]/(b[2 x, 3 y] c[2 x, 3 y])

One could include other contexts in the exclusion besides System, or use the inverse and test only for user symbols existing in the "Global`" context. Without additional examples my example is as specific as I can make it.

Regarding the unusual evaluation of the ? operator (PatternTest) please see:

• Why doesn't PatternTest work with Composition?