Trump's message is that Obama went to the mosque because he is personally foreign or Muslim, or sympathetic to Islam, and Trump is on record as saying that Muslims should be treated with suspicion and fear and barred from entering the country.
Rubio's message is that Obama went to the mosque because he has an agenda to "pit people against each other" and to divide Americans "along ethnic lines and racial lines"; that this constitutes or contributes to a climate of hostility against Christians.
Rubio further seems to be suggesting that anti-Muslim bigotry is a non-problem on par with sports rivalries; and that challenging this bigotry somehow undercuts the effort to address "the bigger issue," which is "radical Islam," and that this is the real threat.
Rubio's implied message is not just that anti-Muslim bigotry is overstated, but that efforts to combat bigotry are worrying because they "divide" Americans and because they enable the "radical Islam" that threatens Americans — and which Rubio has previously said credibly threatens the destruction of the United States itself.
Rubio did not explain why giving a speech against Islamophobia is in tension with the "bigger issue" of defending against radical Islam. But it does not take tremendous imagination to hear the dog whistle that accommodating equal rights for American Muslims will somehow hurt our effort to track down terrorists, which itself suggests that all Muslims should be treated as second-class citizens.
If you want to be sympathetic, you could argue that Rubio sees combating Islamophobia as an unnecessary distraction. But unless you assume that all Muslims are at least potentially linked to "radical Islam," or that Islamophobia is a useful tool in fighting terrorism, it's not clear why Rubio sees the two issues as connected. The sympathetic reading doesn't look much better here.
At one point I thought Rubio was quite an appealing candidate, but I find I don't trust him. He's inconsistent and he seems too ready to pander to the xenophobia of the American Right. After making these comments, Rubio really needs to visit a mosque to demonstrate that he cares about Muslim voters.
Regarding the comments made here, they are the sort of comments that can be quite regularly seen in right-wing discourse about Islam. On the one hand, conservative writers want to say that Muslims should not be the victims of bigotry, yet on the other hand they seem more ready to criticise those who are concerned about Islamophobia. I think it comes down to a lack of moral courage. Conservative writers and politicians fear that if they start talking about Islamophobia, they will be accused of being liberal.