If a college/ university made false claims on its website, should you still consider studying there? The school I'm taking about here is regionally accredited. The problem is, on its website, it falsely claims to be a member of two different international academic associations. Should I look for a different school just because of this? 

PS: I asked these academic associations through email if the school is any way related to or affiliated with them at any time. They gave me a negative reply.
Are you sure this isn't a mistake or misunderstanding from either the university or the association?

I would recommend contacting the department or university. I try to give people the benefit of the doubt with this type of thing but are you sure this is a reputable school? Accreditation is a vague thing and varies wildly in how it is regulated and who accredits it, especially across different countries. 

I'm a little surprised that you contacted the association directly. I myself never pay attention to professional associations and don't know anyone who does (at least not enough to investigate the claim). 

But again, if this is important to you, I would recommend giving the university a chance to clarify by contacting them. You must remember, the people making the website or handling the accreditations most likely aren't the professors teaching the courses. I would also recommend looking into the reputation of this university more if this is indeed true.

EDIT: Many diploma mills/for-profit schools are "accredited" but that doesn't mean they are reputable, so beware.