I mean, I can't say it plays no part, but there are ways to lessen the tax disparity. For instance, if a player gets a signing bonus (which can be up to 15% of the contract) he can have that taxed in whatever state he claims residency. So if he claims Florida, no taxes right there on 15%. Most states tax visiting players, so essentially his home team's state only gets to tax half of his salary, and the other 50% he would have paid no matter which team.
It's a little more nuanced of course, but if a player is debating signing for $10 million with the Celtics (income tax) or Heat (no tax), he would:
1) Get a signing bonus of $1.5 million made untaxable by living in a tax free state.
2) Pay approximately the same amount of taxes with either team on $4.25 million, due to road games.
3) Pay a 5.2% income tax on his remaining 4.25 million, for a tax bill of $221,000. Now, that's not nothing (certainly more than I make in a year), but its 2.2% of his salary, not 5.2%. At the end of the day, I have to imagine its only a factor in a small minority of decisions. And unless you have a no-trade clause, it should be, since you could see your tax rate change due to a trade.