Most of what I wanted to say has been covered, but OP the lecturer was not being racist as Islam is a religion not a race. I am constantly
at how many teachers think that any criticism of Islam is racist.
The establishment of a world wide Caliphate (i.e. everyone on the planet becoming a Muslim) is one of the goals of Islam, therefore what she said is correct, however far down the list it might be after the Five Pillars. You need to be sure of your ground before you challenge her by going to the HoD, as you are factually incorrect on two points here and will end up looking very stupid.
I'm a teacher and I think immigration should be curbed (infrastructure reasons); I have worries about Sharia and the attempts to establish parallel courts in the UK (have had those worries since the mid 80s), and I agree with her that multiculturalism can be taken too far.
As to your assertion that you will value every student equally, you won't, believe me. It's difficult to value every child the same when there are those who steal from you, are foul mouthed, threaten others with assault, key your car, force others into unpleasant sexual acts etc and all these things can and do happen.
You will also find intolerance everywhere in the teaching profession so get used to it. Other teachers will be intolerant of your PC views (I would be and would have avoided you like the plague); teenagers are notoriously intolerant if they don't like you, and you may be dealing with that all day. We live in a society that has freedom of speech, and a right to express your views. When we have had discussions in the classroom like you have had in your lectures, several students have expressed exactly the same views as your lecturer, except far more trenchantly, and whilst one can debate the issue with them, they are as entitled to their point of view as any one else is. All we can do as teachers is to raise questions that challenge their views and hopefully prod them to consider another take on the situation. If they leave a lesson asking why do I think 'x', then you've done your job. You are not the thought police.
Inclusion is a very wide concept - it covers everything from SEN, physical handicaps, to differing religions and races and to study how we deal with that in the classroom is a good thing. You will be challenged on inclusion though by your students if you are going to teach secondary, so you had better learn different responses other than a knee jerk complaint.
All you can do as a teacher is your best for the students you teach, but that will be in the face at times of wanting to boot the buggers out of your classroom, or heaving a sigh of relief when they leave in Year 11 and you never have to see them again in your life. Others you will be sad to see go and will have really enjoyed teaching.