Look, "be yourself" has nothing to do with making imitations or parodies for the sake of entertainment.
It has more to do with - don't contend to do a lot of stuff that does not fit your personality. Don't force yourself to smoke cigs, with the bad boys, if you aren't a cig-smoking bad boy, for example.
When it comes to dating it is always important: Don't pretend that you are full of brawly mannerisms that aren't really yours, because you are creating a false foundation for the girl to like you on - she might like your faked attributes, rather than your real ones.
So, yes, in dating, be yourself, because you want your partner to enjoy your company at your most honest and raw. But yeah, again, when it comes to aspies, most women want a manly man full of non-aspie traits. Many women, luckily, also want a more calm, collected, laid back and intelligent man.
Sadly, next to no women want a terrified, stuttering, helpless man
For that person the solution would not be to fake anything, but to gain some life experience, change who he is - and thus, still be himself but an improved version of himself. We do that all the time, growing up, improve