Welcoming Muslims and LGBT+ people doesn't mean we need to pick one over the other.
Once upon a time, people thought the Democrats couldn't welcome both African-Americans and Hispanics, "because they hate each other."
Once upon a time, people thought the Democrats couldn't welcome both the religious Civil Rights advocates and the Atheists.
etc.
Yeah, but many Democrats view opponents of gay marriage as no different than the KKK. It's hard to see how they would tolerate immigrants with those views.
It's interesting how you seem genuinely incapable of comprehending the concept of someone supporting the rights of people who don't agree with them.