Interesting question that for sure is always timely yet a variation of one of the oldest questions around. If there is a God why would he allow/create evil.
The notion of religionist seems kind of new. Two types to my understanding. Just a regular old adherent to a religion and second a religious zealot whacko who create hate crimes and speech against anyone outside their comfort zone of their religion.
One really cool interesting "religion" believes in a tale of Pandora's box. You may want to look into that.
I think in general you have to look at the natural world different that man. All the "pests" you have mentioned have a role to play in a particular ecosystem. I do not think we say that a mosquito is bad per se. A tiger killing a cute little monkey is not bad or good it just is.
Your question reminds me of those pests called bees. One sting can kill an allergic person. And yet we get rid of them and our whole system of pollenation gets really badly hurt.
Mosquitoes are really a big part of an ecosystem - Birds to Frog to fish and other insects eat all stages of a Mosquito. And wild horses do not have such a problem with pests. That is a man creation.
Fleas and ticks are similar. Other animals eat them and that is good.
So the damage or irritation to a horse is only because man keeps them domesticated. The whole farm type deal with pens and corrals keeping them in is not good.
As for bacteria -- well it is very clear we have thousands of different types in our bodies. They aid everything from digestion to skin health.
As far as I know viruses are kind of like predators. They help to thin out the unhealthy - one of those evolution type deals which man loves to fight against.
So being a Christian religionist I would say that all creatures on earth have a purpose. All things great and small are here for a reason, whether we know it or not. God created the building blocks for life. I really like the earth. Problems? Of course, but I would not go around messing with it.
I love riding horses but if they are kept in close stalls I think the pest is the owner.