Find Abecedarian Words An Abecedarian Word is a word whose letters are in alphabetical order. Your goal is to write a program that outputs all abecedarian words from a given lexicon.
Rules:

Standard Loopholes are forbidden.

If a word contains punctuation, diacritical marks, or any characters other than ASCII alphabet characters (A-Za-z), remove the entire word.

Words that are abecedarian in ASCII are not necessarily abecedarian for this challenge. For example 'Maddox' shouldn't be considered abecedarian.

Your program should work with any lexicon, but for testing purposes, this one can be used. (If my code works properly) It contains 588 587 abecedarian words that follow the above rules. The lexicon does not count towards your byte total. https://gist.githubusercontent.com/wchargin/8927565/raw/d9783627c731268fb2935a731a618aa8e95cf465/words

As per the request of @Olivier Grégoire, here are the Abecedarian words from the lexicon:
A Abbott Abby Abe Abel Ac Acrux Aden Ag Ainu Al Alps Am Amos Amy Ann Apr Ar Art As At Au Av B BMW Be Begin Bell Bellow Ben Benny Benz Berry Bert Bess Best Betty Bi Biko Bill Billy Bk Blu Boru Br Btu C Cd Celt Cf Chi Chimu Chou Ci Cl Cm Co Coors Cory Cox Coy Cr Crux Cruz Cs Cu D Dee Deimos Deity Del Dell Dem Denny Depp Di Dino Dior Dis Dix Dot Dow Dr E Eggo Elmo Eloy Emmy Emory Enos Er Es Eu F Finn Finns Flo Flory Fm Fox Fr Fry G Gil Gill Ginny Gino Ginsu Gipsy Guy H Hill Hiss Ho Hz I Ill In Io Ir It Ivy J Jo Joy Jr K Knox Kory Kr L Ln Lot Lott Lou Lr Lt Lu Luz M Mn Mo Moor Moors Mort Moss Mott Mr Mrs Ms Mt N Nov Np O Oort Orr Os Oz P Pt Pu Q R Ru Rx S St Stu T Ty U V W X Y Z a abbess abbey abbot abet abhor abhors ably abort abuzz accent accept access accost ace aces achoo achy act ad add adder adders adds adept ado adopt ads adz aegis aery affix afoot aft aglow ago ah ahoy ail ails aim aims air airs airy all allot allow alloy ally almost alms am ammo amp amps an annoy ant any apt art arty as ass at ax ay b be bee beef beefs beefy been beep beeps beer beers bees beet befit beg begin begins begot begs bell bellow bells belly below belt bent berry best bet bevy bill billow billowy bills billy bin bins biopsy bit blot blow boo boor boors boos boost boot booty bop bops boss bossy bow box boy brr buy buzz by c cell cello cellos cells cent chi chill chills chilly chimp chimps chin chino chinos chins chintz chip chips chit choosy chop choppy chops chow city clop clops clot cloy coo coop coops coos coot cop cops copy cost cosy cot cow cox coy crux cry cs d deem deems deep deeps deer deers deft defy deity dell dells demo demos den dens dent deny dew dewy dill dills dilly dim dims din dins dint dip dips dirt dirty dis diss ditty divvy do door doors dopy dory dos dot dotty dry e eel eels eery effort egg eggs egis ego egos eh ell ells elm elms em empty ems emu envy err errs es ex f fill fills filly film films filmy fin finny fins fir firs first fist fit fix fizz floor floors flop floppy flops floss flow flu flux fly foot fop fops for fort forty fox foxy fry fuzz g ghost gill gills gilt gimpy gin gins gipsy girt gist glop glory gloss glossy glow gnu go goo goop gory got gs guy h hi hill hills hilly hilt him hims hint hip hippy hips his hiss hit ho hoop hoops hoot hop hops horsy hos host hot how i ill ills imp imps in inn inns ins is it ivy j jot joy k kW knot knotty know ks l lo loop loops loopy loot lop lops lorry loss lost lot low lox ls m moo moor moors moos moot mop mops moss mossy most mow ms mu my n no nor nosy not now nu o oops opt or ow ox p pry psst q r rs s sty t tux u v w x y z

This is code-golf, so the shortest code in bytes wins!
Jelly, 9 bytes
fØẠŒlÞ$ƑƇ

Try it online!
-3 bytes thanks to Nick Kennedy
fØẠŒlÞ$ƑƇ  Main Link
        Ƈ  Keep elements that are
       Ƒ   Invariant when
.[][.]$    Last two links combined, but [ØẠ][ŒlÞ] is an LCC, so it takes another
f          Filtered to keep
 ØẠ        Alphabetical characters
     Þ     And sorted by
   Œl      Lowercase

Basically, &quot;keep elements that are invariant when you filter out non-alphabetical characters and sort alphabetically&quot;. Jelly's sort is stable.