Palatalization of the initial "s" in words starting with "str-"

Sometimes I hear native speakers pronounce the s at the beginning of a word as [ʃ]. For example, straight as [ʃtreɪt], or struggle as [ʃtrʌɡl]. It sounds like German words.

Is it a certain English dialect, a specific accent, or just an idiolect?

Palatal vowels (i), semivowels (y), and liquids (r) often influence the sound of preceding consonants, a process called palatalization. This is most obvious with dental consonants like t and s, which typically become tch and sh. For example, train often sounds like tchrain.

Palatalization is consistent for some English forms, like the shun sound of the -tion suffix. It is weaker or inconsistent for others, like the tr- and str- consonant clusters. Native speakers generally don't notice the variation unless you exaggerate it – train and tchrain are allophones. However, the subtle palatalization of straight could easily sound like shchrait to a non-native speaker.

You're absolutely right, there is a subtle sh sound. I've just tried it myself and I can detect different positions of my mouth and tongue as I say str words, compared to words beginning simply with s (excluding sugar and sure of course) and other s and consonant clusters. I have no knowledge as to whether this is more marked in different regions, but I guess that as a non-native speaker you have tuned into this subtle variation whereas a native speaker would hardly notice any difference. The r sound is more of a vowel sound than a consonant in English and my mouth seems to anticipate this as it says the str.