Having anxiety shouldnt be a reason for you not to be in a relationship, but Anxiety can make relationships difficult.
Imagine being in a relationship where one of you is religious and the other one isnt. Well unless you understand that persons view in life and can work together with out using it to debate or ague then you have a great chance of your relationship working.
Please dont think that im saying that you both need to be identical in your thinking and who you are, as that would be boring.
In my personal experiance, suffering with anxiety has made looking or keeping a relationship tottaly impossible because the people i have met dont get the difficultes anxiety can cause and throw up in a small amount of time.
I like to hide away when things become hard with anxiety and im less likely to speak or i need time alone.
All these things cause an issue when in a relationship.