"fear...of what the neighbors will think"
While Epicurus would not have advised fearing what our neighbors might think, he definitely did not recommend ignoring their opinions.
His advice was to live so as to avoid attracting either envy or contempt.
And also according to Diogenes Laertius' Lives:
The wise one will also pay just enough attention to their reputation as to avoid being looked down upon. (X.120, my own translation)
Hicks: He will pay just so much regard to his reputation as not to be looked down upon.
Yonge: He will show a regard for a fair reputation to such an extent as to avoid being despised;
Original text: εὐδοξίας ἐπὶ τοσοῦτον προνοήσεσθαι,
εὐδοξίας good repute
τοσοῦτον so far as
Provide for good repute for as far as...
ἐφ᾽ ὅσον μὴ καταφρονήσεσθαι:
καταφρονέω look down upon, think slightly of
So, the translations are accurate.