Adedeji, 28, recently quit the show after accusing showrunners of enabling “behind the scenes racism”, in response to their public support for the Black Lives Matter movement.
Her comments resulted in an apology from the soap and its pledge to “stamp out discrimination”.
Clapham, who played Freddie Roscoe on the soap between 2013 – 2017, tweeted: “Dear @chezLysette if supporting a former castmate, whilst she speaks of being racially discriminated against, makes me a traitor... then so be it.
“As for embittered, you’re currently finishing (finished) where I started out. Salty much? – Best, CC/FR.”
In the messages, Lysette, 56, appears to criticise her fellow co-stars for supporting Adedji, and comments: “Sorry, but we’re not going to have a job to come back to if this stuff keeps being disseminated.”
She had previously written: “Well to be fair, they both have that embittered, traitor vibe going on,” apparently in response to Clapham expressing support for Adedeji.
In a tweet on 7 June, Lysette responded to a fan expressing disappointment at her silence over Adedji’s comments about on-set racism: “Oh I will speak.. from a place of compassion and FACT. But I will NOT be bullied into safe, white, knee jerk rhetoric.”
Adedeji responded to Clapham’s tweet: “@chezLysette you are actual trash.. Charlie, you are a King and a true ally!! Love you my bro! X x.”
Lysette has not yet responded to Adedji or Clapham on social media.
The Independent has contacted a Hollyoaks representative for comment.