Can this CFG be written into an equivalent LL(1) grammar?
The comment above is correct. What is referenced here is generally called a "first-follow set clash" and occurs when a non-terminal is nullable, and has non disjoint first and follow sets. You can try to remove these by substituing for the nullable non terminal (shown for your grammar below). However, this process might result in a loop. If that happens, your grammar can't be transformed to LL(1).

Note that . simply denotes esp.

S → a S b S
|   c S2 S
|   d S1 S
|   .
S1 →    a S b S1
|   c S2 S1
|   d S1 S1
|   c .
S2 →    a S b S2
|   c S2 S2
|   d S1 S2
|   d .

S2 =    S d. (uh-oh, we've gone in a loop here)
S1 =    S c.