This is often cited as when the show jumped the shark and it seemed to be ill received by the masses.

Is it due to the storyline being so dramatic and the show was supposed to be a lighthearted family comedy?

The storyline revealing Frank Mitchell as Dorian’s biological father (Season 5, Episode 14, "Secrets and Lies") is widely considered the moment Moesha "jumped the shark" because it fundamentally dismantled the show's moral core for the sake of forced drama.
The backlash was primarily driven by these factors:

Character Assassination: Frank was established as a strict, high-moral authority figure and a solid Black father role model. The reveal that he had an affair while his first wife was alive—and then hid the resulting child as his "nephew" for 17 years—made him appear hypocritical and deceitful.

Destruction of Family Dynamics: The plot twist shifted the show from a relatable coming-of-age sitcom into a soap opera. It caused a permanent rift, leading Moesha to move out and Dee to question her entire marriage.

Cast Dissent and Departures: The actors were "vehemently against" the storyline. Sheryl Lee Ralph (Dee Mitchell) was so dissatisfied with the direction that she eventually left the series, stating the plot "shot it all to hell".

Poor Character Execution: Many fans felt Dorian (played by Ray J) was an unlikeable "add-on" character who never learned from his mistakes, making the massive upheaval of Frank's character feel "unnecessary" and unrewarding for the audience.

The storyline ultimately led to a much darker final season that ended on a notorious cliffhanger involving a kidnapping and an unidentified pregnancy.