To the extent that racism was/is a factor in both careers, yes, but that's as far as it goes. The degree of the racism experienced is orders of magnitude apart. And aside from that, Jackie and Serena are VERY different - both personally and professionally.
It's a well known fact that Jackie was asked by Branch Rickey to keep his mouth shut for three years, take the shit that would come his way, citing it was for the greater good. If Jackie was "well behaved" then it would open the door for other black players. Jackie, by and large, cooperated and held his tongue. As a side note: this was contrary to Jackie's character as a "take no shit" hot head, and many feel that this is what led him to an early grave. Of course, after three years, Jackie let the cap off and was cursin' white players out, spikin' 'em if need be and basically fought back
Serena, on the other hand, came into the game not holding anything back. Talkin' big and backin' it up. There was nothing, demuring, modest or reserved about her. THAT'S why much of the establishment had a problem with her. They were looking for Jackie Robinson and got Serena J. Williams.
Personally, Jackie Robinson was a very vocal conservative. Yes I know. More blacks were Republicans back then, etc, etc, which is why I didn't say he was "Republican." He was CONSERVATIVE. He was very critical of Paul Robeson helping to organize unions and testified before HUAC regarding the issue.
In addition, Jackie, while a good ball player, outside of gargantuan historical contribution to the game, couldn't be considered an ATG on the level of Serena Williams. There were plenty of black players at that time who had more ability than Jackie. Serena, we all know, is peerless.
Also, the level of crap that has come Serena's way doesn't even remotely compare and is almost rendered meaningless when looking at the sea of shit that Jackie had to wade through for the first several years of his career.
There was a time when I thought the best comparison to Serena was Ali, but even that isn't accurate any more. I've now come to believe that there is no parallel to Serena in the sports world. She occupies a slot uniquely hers. She has carved out a kind of "new space" in athletic typology.