From the pilot episode of GG, Bea made a crack about Alan getting his own show like "how did THAT happen?" and by the end of the second season of Growing Pains, Alan had a line slamming Bea: "A lot of men look like Bea Arthur" Did anyone else notice that between the two shows? A second Golden Girls slam was made in the 5th season of GP; "by then I'll look like one of the Golden Girls!" "Don't even JOKE about that Maggie!" I mean damn....serious beef but why? Another similarity is they ran the exact timeframe.

I do not think so. Alan Thicke was the butt of jokes during this time. His late night show was panned by everyone and had low ratings and was cancelled. Its sort of a time capsule to the mid 80s and unless you were there the context is lost. Bea has also been the butt of jokes her entire career. There was a roast once and Bea was just in the audience and the roaster made a comment about Bea having a male sex organ. She sat stone faced while everyone laughed. A year later she purposely went to meet the comedian backstage to commend him for the joke and said "you got me."
It was the writers having fun. There was no reason for bad blood between them.